{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import scipy as sp\n",
    "from scipy import optimize\n",
    "from colorsys import hls_to_rgb\n",
    "\n",
    "def colorize(z):\n",
    "    r = np.abs(z)\n",
    "    arg = np.angle(z) \n",
    "\n",
    "    h = (arg + pi)  / (2 * pi) + 0.5\n",
    "    l = 1.0 - 1.0/(1.0 + r**0.3)\n",
    "    s = 0.8\n",
    "\n",
    "    c = np.vectorize(hls_to_rgb) (h,l,s) # --> tuple\n",
    "    c = np.array(c)  # -->  array of (3,n,m) shape, but need (n,m,3)\n",
    "    c = c.swapaxes(0,2) \n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "###\n",
    "#  Storage format for n:\n",
    "#  n[x/y/z, p/m, x, y]  (3,2, Nx, Ny)\n",
    "#\n",
    "#   x/y/z is direction in valley space\n",
    "#   p/m are the two spins\n",
    "#   x,y = space\n",
    "#\n",
    "#   Right now the energy is just\n",
    "#   E = rho / 2 \\sum_<i,j> (ni - nj)^2 + u_i np^i nm^i - dz (np^z + nm^z)\n",
    "#        + Coulomb\n",
    "#\n",
    "#   TODO: add the Coulomb impurity potential!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  Define all the functions (run once)\n",
    "\n",
    "# #\n",
    "#  The surface area subtended by normal A, B, C is\n",
    "#\n",
    "#  det(A,B,C)/\\sqrt{2 (1 + A.B)(1 + B.C)(1 + C.A)}\n",
    "#\n",
    "#\n",
    "# \n",
    "\"\"\"\n",
    "-------\n",
    "| /| /|\n",
    "|/ |/ |\n",
    "---o---\n",
    "| /| /|\n",
    "|/ |/ |\n",
    "\"\"\"\n",
    "\n",
    "#Six nearest neighbors of site\n",
    "NN = np.array([ [1, 0], [1, 1], [0, 1], [-1, 0], [-1, -1], [0, -1]])\n",
    "num_NN = len(NN)\n",
    "#Which sites included in hopping\n",
    "Lap = [0, 2] #square lattice\n",
    "Z = len(Lap)\n",
    "    \n",
    "Rt = []\n",
    "for a in range(num_NN):\n",
    "    r = 0.\n",
    "    for b in range(a, a+2):\n",
    "        r+= NN[b%num_NN]\n",
    "    r = r/3.\n",
    "    Rt.append(r)\n",
    "    \n",
    "def roll(n, ij):\n",
    "    return np.roll(n, ij, [-2, -1])\n",
    "\n",
    "def X_2_n(X, jac = False):\n",
    "    \"\"\"Convert spherical to n\"\"\"\n",
    "    c0 = np.cos(X[0])\n",
    "    s0 = np.sin(X[0])\n",
    "    c1 = np.cos(X[1])\n",
    "    s1 = np.sin(X[1])\n",
    "    n = np.empty((3,) + X.shape[1:])\n",
    "    n[0] = c0*c1\n",
    "    n[1] = c0*s1\n",
    "    n[2] = s0\n",
    "    \n",
    "    if jac:     \n",
    "        j = np.empty((2,3) + X.shape[1:])\n",
    "        j[0, 0] = -s0*c1\n",
    "        j[0, 1] = -s0*s1\n",
    "        j[0, 2] = c0\n",
    "        j[1, 0] = -c0*s1\n",
    "        j[1, 1] = c0*c1\n",
    "        j[1, 2] = 0.\n",
    "        return n, j\n",
    "\n",
    "    return n\n",
    "\n",
    "def n_2_X(n):\n",
    "    \"\"\"Convert n to spherical\"\"\"\n",
    "    X = np.zeros((2,) + n.shape[1:])\n",
    "    X[0] = np.arcsin(n[2])\n",
    "    X[1] = np.arctan2(n[1], n[0])\n",
    "    return X\n",
    "    \n",
    "def dEtot(X, shape, Vq = None, Vimp = None):\n",
    "    \"\"\"Derivative of total energy in spherical coord\"\"\"\n",
    "    n, jac = X_2_n(np.reshape(X, shape), True)\n",
    "    e, f = F(n, Vq, Vimp)\n",
    "    f = np.einsum('ijaxy, jaxy -> iaxy', -jac, f)\n",
    "    return f.reshape((-1,))\n",
    "\n",
    "def Etot(X, shape, Vq = None, Vimp = None):\n",
    "    \"\"\"Return the total energy E from spherical coord\n",
    "    \"\"\"\n",
    "    n = X_2_n(np.reshape(X, shape))\n",
    "    \n",
    "    nx = np.roll(n, -1, 2)\n",
    "    nxy = np.roll(nx, -1, 3)\n",
    "    ny = np.roll(n, -1, 3)\n",
    "    n_shift = [nx, nxy, ny]\n",
    "    \n",
    "    E = 0.\n",
    "    #Stiffness\n",
    "    for d in Lap:\n",
    "        ij = NN[d]\n",
    "        dn = n_shift[d] -  n       \n",
    "        E += vdot(dn, dn)\n",
    "        \n",
    "    E*=0.5*rho    \n",
    "\n",
    "    #Anisotropy\n",
    "    E += uxy*np.vdot(n[:2, 0], n[:2, 1])\n",
    "    E += uz*np.vdot(n[2, 0], n[2, 1])\n",
    "    E -= dz*np.sum(n[2])\n",
    "    \n",
    "    C = np.empty([2, n.shape[-2], n.shape[-1]]) #Charge in the two triangles per unit cell\n",
    "    for i in range(2): #Loop over triangles\n",
    "        qi = Q(n, n_shift[i], n_shift[i+1])\n",
    "        C[i] = qi[0] + qi[1] #Total charge density  \n",
    "    \n",
    "    phi = 0.\n",
    "    if Vq is not None: #Calculate the potential on each triangle\n",
    "        phi = np.fft.rfft2(C)\n",
    "        phi = np.einsum('ijxy, jxy->ixy', Vq, phi)\n",
    "        phi = np.fft.irfft2(phi, C.shape[-2:])   \n",
    "        \n",
    "    if u:\n",
    "        phi+=u*C    \n",
    "        \n",
    "    if Vimp is not None:\n",
    "        phi += 2*Vimp #because we divide by 2x\n",
    "        \n",
    "    E += np.vdot(C, phi)/2.\n",
    "        \n",
    "    return E\n",
    "\n",
    "\n",
    "def F(n, Vq = None,  Vimp = None, verbose = 0,):\n",
    "    \"\"\"Return the energy E and dE/dn    \n",
    "    \"\"\"\n",
    "\n",
    "    nx = np.roll(n, -1, 2)\n",
    "    nxy = np.roll(nx, -1, 3)\n",
    "    ny = np.roll(n, -1, 3)\n",
    "    n_shift = [nx, nxy, ny]\n",
    "    \n",
    "    E = 0.\n",
    "    F = 0.\n",
    "    #Stiffness\n",
    "    for d in Lap:\n",
    "        ij = NN[d]\n",
    "        dn = n_shift[d] -  n       \n",
    "        e = np.einsum('iaxy, iaxy -> xy', dn, dn)\n",
    "        E += e\n",
    "        E += roll(e, ij)\n",
    "        F += dn\n",
    "        F -= roll(dn, ij)\n",
    "        \n",
    "    E*=0.25*rho #double counted    \n",
    "    F*=rho\n",
    "    \n",
    "    E += uxy*(n[0, 0]*n[0, 1] + n[1, 0]*n[1, 1])\n",
    "    E += uz*n[2, 0]*n[2, 1]\n",
    "    E -= dz*(n[2, 0] + n[2, 1])\n",
    "    \n",
    "    \n",
    "    F[:2] -= uxy*n[:2, ::-1]\n",
    "    F[2] -= uz*n[2, ::-1] #Easy plane\n",
    "    F[2] += dz\n",
    "\n",
    "    \n",
    "    C = np.empty([2, F.shape[-2], F.shape[-1]]) #Charge in the two triangles per unit cell\n",
    "    dC = np.empty([2, 3, 3, 2, F.shape[-2], F.shape[-1]])\n",
    "    for i in range(2): #Loop over triangles\n",
    "        qi, dC[i] = dQ(n, n_shift[i], n_shift[i+1])\n",
    "        C[i] = qi[0] + qi[1] #Total charge density  \n",
    "\n",
    "       \n",
    "    if Vq is not None: #Calculate the potential on each triangle\n",
    "        phi = np.fft.rfft2(C)\n",
    "        phi = np.einsum('ijxy, jxy->ixy', Vq, phi)\n",
    "        phi = np.fft.irfft2(phi, C.shape[-2:])      \n",
    "        if u:\n",
    "            phi+=u*C           \n",
    "    elif u:\n",
    "        phi = u*C\n",
    "    \n",
    "    if Vimp is None:\n",
    "        Vimp = 0.*phi[0]\n",
    "\n",
    "    for i in range(2):\n",
    "        E += C[i]*(phi[i] + 2*Vimp)/6.\n",
    "        F -= dC[i, 0]*(phi[i] + Vimp)\n",
    "        for a in range(2):\n",
    "            phi_shift = roll(phi[i], NN[a+i])\n",
    "            Vimp_shift = roll(Vimp, NN[a+i])\n",
    "            C_shift = roll(C[i], NN[a+i])\n",
    "            dC_shift = roll(dC[i, a+1], NN[a+i])\n",
    "            E += C_shift*(phi_shift + 2*Vimp_shift ) /6\n",
    "            F -= dC_shift*(phi_shift + Vimp_shift)\n",
    "    \n",
    "    F = F - n*Dot(n, F)\n",
    "\n",
    "    return E, F\n",
    "\n",
    "def cross(A, B):\n",
    "    return np.array( [A[1]*B[2] - A[2]*B[1], A[2]*B[0] - A[0]*B[2], A[0]*B[1] - A[1]*B[0]]  )\n",
    "\n",
    "def Dot(A, B):\n",
    "    return np.einsum('iaxy, iaxy->axy', A, B)\n",
    "    \n",
    "def Q(A, B, C):\n",
    "    \"\"\"Area / 4 pi subtendended by unit vectors A, B, C\"\"\"\n",
    "    ns = [A, B, C]\n",
    "    d = Dot(A, cross(B, C))\n",
    "    angs = [1 + Dot(ns[(j-1)%3], ns[(j+1)%3]) for j in range(3)] \n",
    "    denom = np.sqrt(2*np.prod(angs, axis = 0))\n",
    "    return 2*np.arcsin(d/denom)/(4*np.pi)\n",
    "\n",
    "def dQ(A, B, C):\n",
    "    \"\"\" Differential dQ\n",
    "    \n",
    "        Return Q, dQ\n",
    "        \n",
    "        dQ has shape [3, 3, 2, nx, ny] where the first 3 refers to dQ/dA, dQ/dB, dQ/dC\n",
    "    \"\"\"\n",
    "    ns = [A, B, C]\n",
    "    dots = np.array( [Dot(ns[(j-1)%3], ns[(j+1)%3]) for j in range(3)])\n",
    "    d = Dot( A, cross(B, C))\n",
    "    denom = np.sqrt(2*np.prod(1+dots, axis = 0)) \n",
    "    f = np.empty((3,) + A.shape)\n",
    "    for j in range(3):\n",
    "        d0 = dots[j]; d1 = dots[(j+1)%3]; d2 =dots[(j+2)%3] ; \n",
    "        f[j] = ns[(j+1)%3]*(1 - (d0+d1)/(1+d2)) +  ns[(j+2)%3]*(1 - (d0+d2)/(1+d1))\n",
    "        #f[j] = f[j] - ns[j]*Dot(ns[j], f[j])\n",
    "    return 2*np.arcsin(d/denom)/(4*np.pi), -f/d/(4*np.pi)\n",
    "\n",
    "def q(n):\n",
    "    f =  Q(n, np.roll(n, -1, axis = 3), np.roll(n, 1, axis = 2)) \n",
    "    f += Q(n, np.roll(n, 1, axis = 2), np.roll(n, 1, axis = 3)) \n",
    "    f += Q(n, np.roll(n, 1, axis = 3), np.roll(n, -1, axis = 2)) \n",
    "    f += Q(n, np.roll(n, -1, axis = 2), np.roll(n, -1, axis = 3)) \n",
    "    return f/2.\n",
    "\n",
    "\n",
    "def plot_n(n, w = 0):\n",
    "    fig = figure(figsize = (12, 4))\n",
    "    subplot(1, 3, 1)\n",
    "    imshow(np.angle(n[0, w, :, :] + 1j*n[1, w, :, :]), origin = 'lower', cmap = cm.RdBu, interpolation = 'bicubic')\n",
    "    xlim((90,110))\n",
    "    ylim((90,110))\n",
    "    title(r'$\\theta$')\n",
    "    subplot(1, 3, 2)\n",
    "    imshow(n[2, w, :, :], origin = 'lower',  vmin = -1, vmax = 1, cmap = cm.RdBu, interpolation = 'bicubic')\n",
    "    xlim((90,110))\n",
    "    ylim((90,110))\n",
    "    #colorbar()\n",
    "    title(r'$z$')\n",
    "    subplot(1, 3, 3)\n",
    "    rho0 = q(n)\n",
    "    scale = np.max(np.abs(rho0))\n",
    "    imshow(rho0[w].T, origin = 'lower', cmap = cm.RdBu, vmin = -scale, vmax = scale, interpolation = 'bicubic')\n",
    "    xlim((90,110))\n",
    "    ylim((90,110))\n",
    "    #colorbar()\n",
    "    title(r'$n \\, dn \\times dn$')\n",
    "    \n",
    "def take_stats(xk):\n",
    "    stats.append(Etot(xk, X.shape, Vqr) - E0*Nx*Ny)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sublattice splitting in units of EC 0.0884653846153846\n",
      "Rs 0.6409060485485181\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-4-68004658e3bd>:46: DeprecationWarning: `np.complex` is a deprecated alias for the builtin `complex`. To silence this warning, use `complex` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.complex128` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  Vqr = np.zeros((2, 2) + qx.shape, dtype = np.complex)\n",
      "<ipython-input-4-68004658e3bd>:53: RuntimeWarning: invalid value encountered in true_divide\n",
      "  v = (2*np.pi*EC)*(1 - np.exp(-2*D*qs))/qs\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vort: -1.0\n",
      "Initial R: 1.0485301987824283\n",
      "Initial total energy: 1.478034225118087\n",
      "Px: -0.004049527766406352\n",
      "Dz 7.039851627032085\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize simulation\n",
    "\n",
    "Nx = 201 #Size of grid (torus)\n",
    "Ny = 201\n",
    "    \n",
    "x = np.arange(Nx) - Nx/2.\n",
    "y = np.arange(Ny) - Ny/2.\n",
    "x, y = np.meshgrid(x, y, indexing = 'ij')\n",
    "z = x + 1j*y\n",
    "r2 = x**2 + y**2\n",
    "r = np.sqrt(r2)\n",
    "\n",
    "#Energy is measured in units of e^2 / 4 pi eps L_M\n",
    "#Space in measured in units of the grid-spacing \"a\"\n",
    "LM = 10.  #ell_B in grid units. \n",
    "nm = LM/10.4 #nm in grid units at B = 6T\n",
    "D = 40*nm   #gate distance in grid units\n",
    "ECa = LM   #ECa = e^2/(4 pi eps a) in units of e^2/(4 pi eps ell_B) ---> ell_B/a \n",
    "u = 0     #hubbard-U\n",
    "\n",
    "\n",
    "#Set anisotropy parameters\n",
    "Z0 = 0.34 #Target bulk Z polarization\n",
    "gxy = -9.\n",
    "gz = 2.\n",
    "\n",
    "Uxy = gxy*(0.246*nm/LM)/(2*np.pi*LM**2) #u_xy\n",
    "Uz = gz*(0.246*nm/LM)/(2*np.pi*LM**2)   #u_z     \n",
    "Dz = Z0*(Uz - Uxy) #Sublattice splitting\n",
    "\n",
    "print (\"Sublattice splitting in units of EC\", (2*np.pi*LM**2)*Dz)\n",
    "rho = 1./16./np.sqrt(2*np.pi)   #Elastic constant, Sondhi Eq 6 (we use rho/2)\n",
    "\n",
    "#r2 = (x-15)**2 + y**2\n",
    "r2 = x**2 + y**2\n",
    "\n",
    "#Impurity potential\n",
    "Vimp = 0*ECa/np.sqrt((2.*LM)**2 + r2) #TODO convolve with LLL gaussian\n",
    "#Vimp = x/10.\n",
    "\n",
    "#Make the Coulomn interaction potential\n",
    "qx = (np.mod(np.arange(Nx) + Nx//2, Nx) - Nx//2)*(2*np.pi/Nx)\n",
    "qy = np.arange(0, Ny//2+1)*(2*np.pi/Ny)\n",
    "qx, qy = np.meshgrid(qx, qy, indexing = 'ij')\n",
    "\n",
    "Vqr = np.zeros((2, 2) + qx.shape, dtype = np.complex)\n",
    "\n",
    "#One gate screened Coulomb. \n",
    "def vq(qs, EC = 1., D=20., LM = 1.): \n",
    "    if D == np.inf:\n",
    "        return \n",
    "    \n",
    "    v = (2*np.pi*EC)*(1 - np.exp(-2*D*qs))/qs\n",
    "    v[qs==0.] = 4*np.pi*D*EC\n",
    "    return np.exp(-0.5*(qs*LM)**2)*v ##LL form factor\n",
    "\n",
    "Lam = 1\n",
    "for gx in range(-Lam, Lam+1):\n",
    "    gx*=2*np.pi\n",
    "    for gy in range(-Lam, Lam+1):\n",
    "        gy*=2*np.pi\n",
    "        qs = np.sqrt((qx+gx)**2 + (qy+gy)**2)\n",
    "        for i in range(2):\n",
    "            for j in range(2):\n",
    "                dr = Rt[i] - Rt[j]        \n",
    "                Vqr[i, j] += np.exp(1j*((qx+gx)*dr[0] + (qy+gy)*dr[1]))*vq(qs, ECa, D, LM)\n",
    "\n",
    "                \n",
    "#Initialize the NLSM\n",
    "n = np.empty((3, 2, Nx, Ny))\n",
    "\n",
    "#Mainly point in XY plane\n",
    "X0 = np.sqrt(1 - Z0**2)\n",
    "n[0] = X0\n",
    "n[1] = 0.\n",
    "n[2] = Z0\n",
    "\n",
    "#But force a skyrmion into one of them!\n",
    "\n",
    "#Rs = LM/2.\n",
    "g = np.abs(Uxy)*2*np.pi*LM**2\n",
    "if g > 0:\n",
    "    Rs = np.max([LM*(0.0867/(g*np.abs(log(g))))**(1/3.), 1.])\n",
    "else:\n",
    "    Rs = LM/2.\n",
    "\n",
    "print (\"Rs\", Rs/LM)\n",
    "#th = np.arccos(1 - 2*np.exp(-r/Rs))\n",
    "th = np.arccos((r2 - Rs**2)/(r2 + Rs**2))\n",
    "\n",
    "phi = np.pi*0. #orientation of Z-polarization dipole\n",
    "c, s= np.cos(phi), np.sin(phi)\n",
    "\n",
    "n[0, 1] = np.sin(th)*(c*x + s*y)/r\n",
    "n[1, 1] = np.sin(th)*(c*y - s*x)/r\n",
    "n[2, 1] = np.cos(th)\n",
    "\n",
    "Rot = np.array([[Z0, 0, X0], [0, 1, 0], [-X0, 0, Z0]])\n",
    "\n",
    "n[:, 1] = np.tensordot(Rot, n[:, 1], axes = [[1], [0]])\n",
    "\n",
    "n+= 0.01*(np.random.random(n.shape) - 0.5)\n",
    "n = n/np.linalg.norm(n, axis = 0)\n",
    "plot_n(n, w = 1)\n",
    "\n",
    "Auc = 1.\n",
    "Atr = 1/2.\n",
    "\n",
    "uxy = Uxy*Auc\n",
    "uz = Uz*Auc\n",
    "dz = Dz*Auc\n",
    "\n",
    "e, f = F(n, Vqr, 0*Vimp)\n",
    "rho0 = q(n)\n",
    "C = rho0[1] + rho0[0]\n",
    "print (\"Vort:\", np.sum(C))\n",
    "R2 = np.vdot(r2, C)/np.sum(C)\n",
    "if dz != 0.:\n",
    "    E0 = uxy - dz**2/(uz - uxy)\n",
    "else:\n",
    "    E0 = uxy\n",
    "E = np.sum(e) - E0*Nx*Ny\n",
    "\n",
    "print (\"Initial R:\", np.sqrt(R2/2)/LM)\n",
    "print (\"Initial total energy:\", E)\n",
    "print (\"Px:\", np.vdot(x, C))\n",
    "print (\"Dz\", Dz*50*1000)\n",
    "\n",
    "stats = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.767310184978669e-09\n",
      "5.761008521754804e-09\n"
     ]
    }
   ],
   "source": [
    "#Test accuracy of derivatie\n",
    "X = n_2_X(n)\n",
    "sca = 1.\n",
    "J = dEtot(X, X.shape, Vqr, Vimp*sca)\n",
    "dX = 0.0000001*(np.random.random((X.shape)) - 0.5)\n",
    "dE = Etot(X + dX, X.shape, Vqr, Vimp*sca) - Etot(X, X.shape, Vqr, Vimp*sca)\n",
    "print (dE)\n",
    "print (np.vdot(J, dX))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ef: 0.8748383855929909\n",
      "Charge: -1.0\n",
      "Px: 0.6875563265539706\n",
      "R: 0.6234430578685283\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Find the ground state\n",
    "X = n_2_X(n)\n",
    "res = sp.optimize.minimize(Etot, X.reshape((-1,)), args = (X.shape, Vqr, Vimp), jac = dEtot, method='L-BFGS-B', options = {'maxiter':80, 'gtol':1e-10},  callback = take_stats)\n",
    "print (\"Ef:\", res['fun'] - E0*Nx*Ny)\n",
    "plot(np.array(stats), '.-')\n",
    "xlabel('step', fontsize = 18)\n",
    "ylabel(r'E', fontsize = 18)\n",
    "n = X_2_n(res['x'].reshape(X.shape))\n",
    "\n",
    "rho0 = q(n)\n",
    "C = rho0[1] + rho0[0]\n",
    "print (\"Charge:\", np.sum(C))\n",
    "print (\"Px:\", np.vdot(x, C))\n",
    "R2 = np.vdot(r2, C)/np.sum(C)\n",
    "print (\"R:\", np.sqrt(R2/2)/LM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "0.0011817953489128342\n",
      "-14.748048082087447\n",
      "0.0011773417803551977\n",
      "-14.748049476088251\n",
      "0.0011729571814445023\n",
      "-14.748050859633237\n",
      "0.0011686396879360633\n",
      "-14.748052232922303\n",
      "0.001164387504974749\n",
      "-14.748053596149248\n",
      "0.0011601989162576968\n",
      "-14.74805494950201\n",
      "0.0011560722680164538\n",
      "-14.748056293162938\n",
      "0.001152005957560328\n",
      "-14.748057627309016\n",
      "0.0011479984657241328\n",
      "-14.748058952112068\n",
      "0.0011440483148088855\n",
      "-14.748060267738994\n",
      "0.0011401540847660622\n",
      "-14.748061574351953\n",
      "0.0011363144101029913\n",
      "-14.74806287210855\n",
      "0.001132527964227895\n",
      "-14.74806416116202\n",
      "0.0011287934823534776\n",
      "-14.74806544166139\n"
     ]
    }
   ],
   "source": [
    "#Dumb steepest descent minimization\n",
    "dt = 1.\n",
    "for t in range(100):\n",
    "    e, f = F(n, Vqr, Vimp)\n",
    "    print (np.linalg.norm(f))\n",
    "    n = n + dt*f\n",
    "    n = n/np.linalg.norm(n, axis = 0)\n",
    "    print (np.sum(e))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.31332853432887503"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.pi/2.)/4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(Vimp[100])\n",
    "plot(-C[100])\n",
    "print (np.vdot(C, Vimp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sIbbAvtQ0fsB2xXVRZHyufWRjn7OvPyXiuyQSPCe6rWJbmcu2rkZl6+xKZBuSZn30RLXtfcz91cr5kSa0gclASABJtpGufDwIMjeaPZlcxlhG7Ai2FNW2xbU9+NEXzc6YcCYVW2+MJlrBWKyelgU/to3PKuIOeEzFFeK5kWy3/1JmkByBLdlDVFxP2Zq4Lj2PrQnqHKS+5wjvcwjuOVYSFduKouSyO5HtDm4E4mI7xz6SK7S7Pgn+bGE7AHEQZPZ7EMgkwnCi5G4mEcuXPRr8uGDO7JjesO/NdtWYH9u9p9u5sX2Eotg+X7bPtx2MZDup+uYIbCl6fWk5lrcors8hrJcS1TXanWML8fUjtc05gnup6LaKbUVRctmXyDaDwyxBDcQtJLn2EZ/QdttP8Web7TbuIEggLZpN7uQysCPWzpTnwGAPCfiy/TM/ltlJUu/tsXoTQe1Eh+3txioyaUMY8JiCZCmRtkv1Td9rC+zRrI/OIMk9s3dxvYawPle0O3acIntIgejOFdxbF9vKftFPUMllXyIbg7CghiaiGfBPsR6zj6QI7RaNmNqvO1bAj11pCnU+Hr2zPnotI+ZYTmYRCdFjLUWwC6Pa0j17bB+R97PT9bmp+0JWER+hKHZJrmyfvaW2wG6dtvfMVRLXc0Txlu0jNbzZdhu1BXeplWRpsa0oytVhdyLbkCq2U+wjc4U2YFlGXH82xqI6lFUkFs2epP3zTTTjyyZiLY/82YJoXjK9n6RP7Pu1b9DjeBlONFu2ikgDHmPE0vt5y4SBjma9O+/5AnuUdWTDAszHnsV1bt9zBfKWBXUOxRaRQsFdO7qtYltRlFrsTmTbIhrohAb1f5CTJ6OpJLRPx8F4ICQg20a6fpT7sU9CHhhFpV3LyGTQo+XL9g5+HBrzR6kzItgpekTSQb6osG9ZWo8NeAxFsUuj2adjt+NMIqkCO8V/vWeBfVXE9bmF9bmF+dksIhmCW8W2cg729RdX2QrRPx9E9BYiepiI7rPKnkBEdxPR/f3r4/vyv0NEH7T+tUR0i9DmjxPRH1v1XprSWfte1x7bk+C2f5bnIw/ZQ+w6pzIjWNxyT70jn+q2llehdY7D1ig97tddmwgf2+Ff2/WNj8dTXT62aK1lXzvdQVtwO85Swu5IQWv7KKOJs1+/87Ssh2YkZk7RACz8+bJPxfVj28vjCLjPmz32WKcwtZQ4wt7jw64hsM33ubVsL3a7blsuW7pmj8xFAts+96TjtOkCO7Xt1L6X/EqSM0ZA2i93/1rU6EfufsnvrRl/kfCZ5Xy/cr5bpu0ctnS9KopSl5Rn9DsBvMQpez2Ae5j5ZgD39Otg5l9g5luY+RYA3wvgD5j5g552f9rUZeb3pHbYFtFAutg2Zd06dyK5NSK2q5sqtE+WD6cvPmHtivASWp/gbo9jRXo8jsV16xHXp4eMgOCuOOuJeZfaQDxA2uLzY0+i2c5N2B7wKBGKYkuDHYd9ZB+2lKoPgCfXNXfC2yOwTf9PdR1h3rbhGS6xsWs2hz2K69R6c0T11ikV3qUPKNG6C4ntVDK/x3dip9eroihhoiKbmd8P4LNO8csA3NUv3wXg5cKurwLw1jmdm3bGEb4BsX3aRRDaoai2aSdVaNv7DetDFHrUfSFKnRLNnrwNRkjb0fM2JK5bebmHzM3gjFMJnjzIwn3o5G0O+LHtum499y2TPNYpxISD7cMGplFme6p0V2CbOl3ZsL99rqHotRHpEpu6ZhPZi7hOFXpzxGapqPZFmWv8q9GfnPqpdaP1Kovtkqh2rN09Xq9Xje0/5ipbpdQg/GRmfggA+tcbhDp/G+E/AK8jog/3P5U93leJiG4nonuJ6N4/OT4KYIhEA7LYBqZRbbMtxz7i1rHrdXXbUT9CtpE25y+zg93GVLgHLCOj5WnE2t13Tcx9SLoh+fzY9j22ZTm67Y9kh6PYvn2lbcYmspTANvVtgV3AWa5Z+3r9s3/l6gaZPYnreP/WsY0sHe0+t00k92Em2t4OxLbDKvfYTz/ySE4fFUWJUHc6vx4i+jcAfIGZ7/NU+VkAzwRwC4CHAPyUry1mvoOZb2XmW7/2cHAEtSy2pah2zD7S1Q0LbbbqDcdt0ToiP2YbyY1mT96Tvr510KllxN522u/Y999vESHXKtI66xUw98TQPefoiNHQss8qYhMTz95+BISF68M2/fIJbLfvOQIbGEev2TnuXGpds/b1+tWPe0LwmCXR6xTOLa7PFd3eom3knDaRGu3liO0UcsV2LZa6xz7p+uur91VRrjKl2UU+RUQ3MvNDRHQjgIed7a9E4AmbmT9llonoTQD+l5yDTyej6daHjCDOhDP9H16T7i+YUUTKPIJmqNO3za2bZWTYBkwHIUq5sd2ZIA/CZDNuvdFQdyeF3yRzyKhcSP/XNHKGkRBmohr2JRycchKPnvuWuS8eT6JyWsfnxw5ZRVIj0r4odnBfwYft9WVbIjkksKV9pOh1bOCjh1WvWZulMobUzBaSKv6Sjpf5UDeX1MG9KVw7QzYRu36orqmX2l6wrYSMJEtmIklgM9eroijllP5JeBeAV/fLrwbwTrOBiBoA3wPgbb6d+z8ahlcA8D2Nj2CeWj7cyPapbiSqbbaN1+WItlvHjWi7AyFda4hrG/FlDPFFs22ilpH2OPRf8mVLthET+a7syZ57qzdvv+THbtn2bk8tJe6Nfiyc885zIrwFH7Yvk0hMYJuoq+u/luwhKZlFAqxyzbosYQ1ZK3KdUienXo7AfrR/KJT+1aTGcWrbRGpaSVK+E0sNjoywietVUT+2Mo+UFH5vBfBrAJ5FRA8Q0WsAvAHAbUR0P4Db+nXDiwA8wMyfdNp5MxHd2q/+JBF9hIg+DODbAfz93I77xHbIQgJM7SP2QEe293UGQ5plgyvupYGQPjEdso1ISAMpky0jki/7JLg9d4STdWS5Py/myCZ9nzmSO+hR8mP7rCLHdizi7Ai1TU4U23dDd33YQJnANsv2q88eYrZJFhSbLV6zS1pDom2tIK5T6qSK6qWFdCkl/VrKJhKrEz3Win7tLV6viqLUIWoXYeZXeTa92FP/XwD4N4Xy77OWvzexf9P2+z+YZgIaY/sAxjYSY/8w5Tn2kRbT2SFP06jb263JarrjjC0kXX+FbB6B3xTdlHqdjWQ8Y2QL4GBPlw6ELSPuLJCj9/M4mp7dUylrgprQ/aVUtxthGbKKGKQbb2kUe9JGxId9Wq8gsO3y0baIaNjSNbumNeRctpCa1hJgvt2jlne7ZOIZt+8hu0lNm0isTi0LCdB992paSLZ0vSqKUpd9zfho/f22hfJkFsijMJ26JaZNXTNbZA2hPUy33i+bUkcgG3yOZsmbLc0kacQ7+WZytGd/bJrh9djVc8X1aRr1SjM+Ts5LuO+bMjeziBuxPgr7ps4GKeW8LoliuzYRYPBhSwMdu/OqI7Alr/cZsy0WkyP1zu273pK4LhHVtYR06TFSBbh9bnMFd06dpcV2rl+7oldbUZQdsS+RjemgR5/YFqdT9wyKnCu0u34IUWxTv19PnVJ9MkHMaAr1cXjEiGYAjrhuTwL8RNtake0mPPhxhqCOkZKCThLW5h5r3/vNss8qMl5vk72evnq2TcQ38NFO1detW3UKBfZ4UKT3FHbJ1qLXS28H8oT1OQR1LlKfYsI7V3AvGbk+t9heIwOJMp/tXXnK3tiZyLaERobYDkW15whtYJpVpFtPs42kRrPbdirUu6wn/bptGTFCGuh82W5Z8O0VhLWQReQU9U4gpnkGkWxEpbtdjm6P9omKa38kOzRBjRvFdm0i3flNs4LYubBTBXaKPcQW17k2jC2i4rq8nSX3t8mxjLjHDe2bIrjPEblOFdu1LCSKolwtdiayMRoc6EasAZwEs6kbimqXCu1T205qP9GfjaltJAU7mk2C5YQOw3Fcy0jQl22i1qeo9lSAE7dgcoX1tCwXe0r1kCby20bYW2ey3I4HYtmTz7jkDHgEpjYR08dcgV1qD3Hb2iPnFNhri+slhPW5otu+46SI71TPdY7gniOmY5Hxc1pIFEW5GuxKZDN3AqSxRDQwFdspUW3bPtL2Q/UaK2IbEto4ietBaAMmui7nz7ZtIzbebNPCYMdT5LovC1pGEnzZo/f2eASuOV8HkxN7YcwtNiUaadcb20Z60Z0RyZb82r7jxWwik4GQMwW2ZA+xBedeBfaWotdri+scobw1y0iuXSRXcM8R2xrVVhRlK+xKZBuMEMkV2/Z2c6/3RbVNG6lCW/Rno/X6sN2I9OQcj7KX+7Rf00QtI6Iv2+6DFPmu5MUeCcJRuXV8wfHmG/TYOq+2VcQIN/tG7gpoX2Q6ZbBjyCbiG+gIuEI5X2DHotd7Etq5U1BH21swej1n31rCulRU1xbjS9hFUgT3HLG9tIVEo9pXg/38dVW2zO5E9pEBY3WWxLabYQQYLCSxqHap0DbHG6LNgj8b42i2HZGORbNPk91gSOfXCegEy4jry3YHP1qMvNa22G6XHx4vCSufbSTFKmIv22n7cqPYNrZNRPJh25lEpJkcSwS2FL3ek7gGLscasrS43mJkO3ScGjM5xuosLbbnWkg0qq0oSojdiWxgiG5KYjsU1Za82rlCu9t/nINbGghp+7MNbrYRm1Hua1MmRLM7QT0W6AfXAiJlD/HlyxbEdpDCSLetjVpfuYlIC/f1oyu47f0Eq0juAMhYFDvFhw0sI7B90euCWR/Pzl4E9lrieunI9pLkDHScO4hxKbGtUW1FUZZkVyKbMY4e5IjtkH0kS2iPBjs6GUd8/mwh24h4fk5qDVukn3JlN83IMmL2O1lGXGEvpvJzBj/aZd1OJyEdzCQyI8Jt35/FwYhCNhEJn1Vk2N5OxHYsim0Eto+QD7tEYKfYQ/YmrlO5RHFdQ1iXiOo5Ey3FcAMA8vHTRPccYZsitpfya9eIaiuKcrXYlcg22DfdA5Eotl0LiRTVrim0T8dy/Nldud82YuNGsztvd29BMcdo27BlxJM1JDj40a47YzIa9xbi6oSUe8woHR+P2zGvth+7q1c3kn3qixDF9vmwXYEcE9gl9pCx33v/iXeXFthLiO8lxXV6VPv8n710zJjwjkWvU7fniu2lLCQ1otqKolwtdiWyu0h2t2w0rP2Hzd6WEtUe+bRPJo/EwZB21Drgz5ZsI8FztG5mowGPpxkerUh2v+xaRqK+7NHxBrE9yTCy4IQ0gBPNdmwYbrnPj21bRU77BMS1Ly92zCbi4vqwTZkvA0iOwJbsIZcksC8ter2U0B/qzP+8Y8cpmULd7VdIdM+JXp9bbJ8jqq1sG/3NQanFrkS2jSS2JRuJK7btqLbBjWqfMo9gOjskMBba7kDI6VTqjIltBGnR7PGAx8NQZm33WkZ8vmxAFNsuk7zYhYLbFVTubI/2mpQHG8L2IaJtXsci2pRJAx7ddUlwS9hRbJ8P2xbJvolmUgW2PCnNcD7cOrOC7oStRq9rW0PmR7XThXUNv3ZKG/GBjnHRPSd6PUdsl0auNaqtKMoc9iWyefrHyxbU0jbXQhKLak/sI5gOfBxlLnGnV7f82a5txHAaHOnRuVI020xOQ4fmNAMkHZoky8jIlz0S224u7Yw0fjOi3K6GkiwigJ3GbxqlFjOMWALbLsuyjXgGO0oRbdeHDdQV2FL02hbXexLaa+e9Ppc1ZN4DQJqwXmsQpHTc8GDH1qrnF9y1xbZGtRVF2Qr7EtkWqWLbjWpLXu0soY3mNDOkiVoP9hCPP7srmeTOtrOHjBDyYmMkpMfLIcuIjfFj9wcfBjpaYlsc6ChMrZ6DpAncHNm2vhhHtKdtSFYRV2DbAx7N9vGAyPQo9qjfLUd92N351BHYvuj1VRPYS9hDalpDygV+XFiXDYKcJ8RT7SPpgx3bfntedLtEAK8R1VahrSiKxK5ENiPsyQbCYjtkH5krtIFhgKPtzz71PWIbsf3XUuq+08QzjSWqe4EdyjIy8WXDFdsR60ilWR9bweWWG9GOiTXbKnJqJyKsc6LYIR+2NNDRrLvLtsBOsYf4xPUehPaa9pCa0evaIj4mrtMHQS4T1Q61OydVX2l0Oya2a0a1l7SPKIpytYiGJ4noLUT0MBHdZ5U9gYjuJqL7+9fH9+VPJ6I/J6IP9v/+qadNcf8YdvTzyGMhduRx2jV3m7vPSbj1kWLj02ZPeXtka7kdi6JjO/J5c9utm/JWSvzsntux7f617RC9tsrttu1tbtkII8JsMTba3yl3RRt72vWVY+q5HnVH2OTezKVBj/ay2ez6saVXezkniu2bdGZcRx7oaGcSCaXpkwR2O4p4+wU2t8egwN7KNRv6LgDTa3ayPfJLQ6nwrSWwfW2FjtH9wiJfPym/ruSOJViC1D7E6qS8F3PLH3WufXefnGPHtoXaDLGV61VRlPqkeADuBPASp+z1AO5h5psB3NOvG36PmW/p//2gp83Q/kEkMe0T2/Y2txwYC20jiPnIXqE9WW4d4S0Iaru8a7vtl9tTWduL68l+luDu9jP9sco9rycxbbfrE9uSYAsI6TlIrbpCqxXENTDcwKTUfePXdrKPWU6JYk/67ESxfT7suQK7W28nAtsW1YmR7DuxoWtWYm70ulQgSfiEWC2hZ8SkJCjjQjRPVLv1a/zLOWasjrwtLLZrlOd+xqG25mzzcCc2fr1eJfQ3B6UmUZHNzO8H8Fmn+GUA7uqX7wLw8szjzt0/W2zb5XaZHT20RbUktI2ANsIYGAttu56JZudgR7Pd8mF5EFZtOxbWQ18lQeYT25kCu4L4lu5BE6FtVWqFz89N3edaReybpzv5jO/GmmMTMX2wBzoC8wV29zoV1W5ZKJK91WvWcG57SK3odam4zu1TqsAtEcQl5Bwn56Fhui38IDK3HKj3a0Von9h+Llu/XpXLpeWyf0o6paPZnszMDwFA/3qDte0ZRPQBInofEb2wYP8gPjEtRa/Ndrc81T6SKrSldUC2jaRGs9lE1y0hPYgwIZLdjl8hRTyPjjhzhBq3x7GFxIESBXbapDPTMveZxK4zim4nWEWGun5x7UaxU7BtIr6Bjqf1QoFtXmPR6zbPk73aNWtYyx4iURK9zjtuubj2USqoa0Wsc/uSun1aXk9sS9T23VeOahtWv16Vy6OWWFbRnU7tgY8PAXgaM3+GiJ4P4H8iom9m5j8tbZCIbgdwOwA8gYbuugMguzI5V7Y0ANI3KFLKpy3l0TYT1pymU2/G61L6PneSGrjTnWMctbaziJj19thOcmbbWUZgBkOaVH5uvmxzHHvwIzDZPvoMuHswyJlCPeW6Y0wHxnVCzOqWLWSlh6eJwG5P61JU23fjT4liuzYRs58vk0i3bvqeJ7DtV3c5U1zHqHrN2tfr45/8lFP5UtlDSgRObvQ6rz91bA+p23PrzWlj3oBHzt7my0hybOUBiFK5r21fBpJYP5fIPpLJovfYm266qVI3la1wDhFsH6PeV/0yKI1kf4qIbgSA/vVhAGDmLzLzZ/rl3wLwewC+MXV/CWa+g5lvZeZbv6o5oMXY12ui0ZL32mwflsNRbSAtot0tW+LPGQhp9rNtI26U27SREs2217vX46lezDLSV7IPOl53t7vMsIcwp4lt6fDuoEdz8xtHtLtlySpicAc82su5UexTfy2byCTTiCWkawvstj2OBHZmdpGzXLOj6/VxTwAw3x6SL3TzBsHViF7Xir7a25aIas8h9ZihOqWR7fS6y0a15/zSkvk5rXKPfdL11+f0Udkwa0WZNcI9plRkvwvAq/vlVwN4JwAQ0ZOIunxvRPT1AG4G8MnU/XNorX+G0EBHV1SbcrssVWhLGUeAwZ+daxtxkTKK+AZAjl5dywgCvuzuREV7CDED3CbbQ2Iwxy0krSB2XXHm+rGBsGUktnzqX0YU27WJdOfn+LIrCWzbMuKK64L0fatcs2v4ryVqiKmlRWCq8E4Ra279kn85x4jVydm31kNMat1z+bQzWf0eq+yTLQncLfVlLVJS+L0VwK8BeBYRPUBErwHwBgC3EdH9AG7r1wHgRQA+TEQfAvDPAfwgM3+2b+fNRHRrX8+3fxTJ1ymJbal+KNPIXKEt+bNz0veJ7Qjp/Ibl46hskl2k65zVliPKJJEmpfGrCDP30W3/e+KK7e4itUW1eR0L5+61Ha2Ptwl+bE8UO9cmIg10NOdi1zd1uvX2JJZ9Ax27+kP0OnXw49auWR9bFNhzhV+puPb1LzeiXTOyndNu6kOCb1tq/ZDYTinzldfMPpL7GezlelW2zZYF7Zb7tjRRTzYzv8qz6cVC3bcDeLunne+zlj8j7Z+DLbSND9v86W0wiGV70hp3Bki7TFp3PdpAJ5ZOHm1r0hnXnw3AmfXR/C/PBGnbs0fTqjfNMBGN8V0Dnfe6n3ymbdvpxDSSLxsAjkdwM/Vjc9tMZohcEuZB6Eq4F6S9bu/js4ocrZvmRFxb61IU24fPJgJMBzraMzn6BHa3HLaHuGXussRWr1lDTIDU/KneJ5xS20iNXOfsHyqfsy0F6f2QJmxJPX7IYy1tN9vml7dJXu1Qu7kT2NT0adts/Xq9SuxRB+5JvLZ89Tzb+5rxkafiGRhEly22m9O2ob47MDJbaPei2ghtwBrMeBgLawCTWR+D53YczwJ5cGdxhBHOwwyQh8NhNOhxtM2aYv2ENPixbcQBmOfEHexoaB0RLtlE7GXp1RvJFqLYpTYRd6BjqcCWBjf6Z3usY+U5N1uNXqfXTYui1jhWyjYb3znP3S8kwkOC2t5eQ2ynDIzM21+uu4bQVpQS9iSwDabPV+Wy2JXItomJbTuqberHMo0AprFhPSS0zZTqdtaQU2TbiCvMi2YbAd0CvXDuy08iuhllGeFDL7ptcd4eQe1hmD69PQL2+kYwYnvixbb+krQ8tYl0y2OrSGzAo8HNDhLDF/W2fdjDer7AToleq8AOl88V2P7jldsUlhDXpaI6l9Tod0oE292WI7ZrRLVTRXKJ0Jb6FtpHUeawR4Ftc1Wi2rsT2W7U2o6AutYQwG8hSbWPpAptoPNnm0h046S7G4T4ILQPTgTZjmbjMJQBEIRzK1pGTvuY40+i172NRKK3jeB4BIjQh3H7f/1618jQwYU4Mk8sIrbd3BetDm07LQuzO6ZEsSVBftpHGOhotnftlwlsn7gO5TPfImsK7CXsIfMj4vmiO1dUz7GWxESh3ZeQ4J6bai9VLPuEtttmznFCaf5yI9dzbT6KYrikr9JVENql2UVWRxoAGUrlJw2MTMk0YlsZRrYAN4XfZNbHLq2fL33fUE/ONCKl8zOv03R903qtk6EEvoFyJsNIanS0V5OUGPkdHQrDAAiGGeQ4toFM9vFkGAHkaLUc5Z4K7e5U8qLYNrYot/tqZxIpEdjyIEj3u6ACW2JrAtv9vvnKQuVmQF5IYJt93X9zyGkv1Eff/jnvQ3rZvEGRud+rkgclRZnDJX61jCa4VHYlshnjyDXgF9vSdjsLSU6mEXu5ba0p1Y9ONNSTTWSSvs9J6TeuOxbbkqg25d3rcVrmCjL3xmNmflwwk4hNC45eRG0fMRazffDUjx0S0/aAR6ne3Ch2yIdtt9ctT9MphgS2ebUF9mn/4zAjZ2Eav7PCKBfRSwnsOYJtngAsE9cSNcV0DinHTRHcsTJTXl52HqEdqq9CW6nNpX+lLvX8dmcXAfwWkaFsbAMx292BkamZRoDpYEhgnHHEaxuxso34MPVhzQJpspW4AyBHXm3LMuLO/mjvMxzIyTQyl4Q82iUXTsvTQY9d+TQNX/fapkeyXauHEMX2CexpPfYOdOzWhzzYOQJ7sr8Tud66uE6hRJz4xGhq3bVE2pJirrReDiFrRKhOzqyKc8tq+rSlY5jzqTUgUlFyuFQB6tLy5dlHdhjJnkatpei2tN2Natt17P2kdSm6bUeiuZUj065tJBbNtmeB7Nq1JqLx2EJO+1qzPyZZRYAhom3qVMyVHbKBpOIKY1MWWpbsIXY9Vwy7UWwf7kQ1o21WWbe9XGDb9pDRLxWJebK3TEmUOhTtTW1naYE9N6JdkqfZ3r5kVDvlGKHtoXOrVZbza4Sv7ynH1Yi2cm6u2lfo0s53p5HscdS6KzPr4zpuyj6zzc1AkpLSz45oo50OhATc3Njpafxi0WyTA9vNmT3Oiz1N5UfNdKAjty0okmGEmMH9rI8l3/mUC8U89JiHGCmzyKluO972qEdAS3mzT8uWiPblxY7ZRNy60kBHdyZHezlFYJ/2OU6j29L6Xii1jkicQ2CfI3qd4yOPbZtT1yYWfY1FsEORYGAc2a4fwY5HtX39S21PI9qXyYVpu11zSRHtXUWyJVxPthvZTpleXfJpS+vuNncgpCvC7FkcY9Hs6X7jmR/NqzSVujv7o73P0GgbjGgHCdhCSqZeNxPR+DCZRVqeerndqJOdui/FMgKgKIo9qR/wYXfr/oGMMYHteq/tNnMmpdkSV0Vgp0avpehuSqTYhxttnhNBldoqiWDnRLZ975vUZtl+dS1ANadiVxQfV/krcynnvjuRbYRybACkJLbtbe4+KUJbFOitOxW6bBuJYWcaObVtrdsCWswq0t9EWncqdkuEz6Ekm4gLM4JTqvvoxLb/RiotS5Hs0ayMBVHsmE2kW29nC+yhLdkasjeryNICO+fn/jmWgtgxa4vrFAF7TvGWKrhTy1Oi+HPE97ROfaGd+0uEoqSiX6PLYJd2EUPK7I/u4EazzWcfCVlH4GwzObQBRG0jVgZs7wQ1Jm82t+PJaYYZHC17SOuf/RHofdmNlS/bYDzXx6abXr1tgPYwzA7ZHgF8mfyGt23SY5nkxS5Jk+cyjWKHs4yMyqzBieOIc3oUe9gnbBPp6vinSY8JbP8kNPuzjZxDYKe2IQnseJ1SQVcmKn1lofLSeimUDHoM2THc8hwLSa59RK4zb0Bk6lTsvrqKkoIK7I6W928b2VUkm3kasQbk6LYU2ba32fvZZaGIti+1X8w2YrBtI+L5OSkA3QGQ5lUaACml8hutZ0Q/uT1WiX6nYNL2Da9DZpHj6XW8j+3HBoabqeTTtoW4lLbPJiWK7bOJ+AY6LiGw9xLJDj1XLSWwU+0a5xTYOfaInEiwvW2pqHZK277tOeeTGtWuU+d8ubQVRZnH3i+j3UaypcGPXfk0sh0a/GiXp0S0R4MfnYGQYlo/zyDIcaS7r3Ga5bFryx4AiQNGkequvPWm8uv60J6i4EUIfuuSgZCS2DIT0aRiRPeozGogFsl2BzwOfRvyYucgpfbzieJcgX1JkWyJJQV2Wlm+wC4VeJK4TuljSfncuoZQBDYUwba3l8yy6Itql0SwY8c6Z0Tb7a+ihNi7qFyCPUe0dxXJBsZR5KFs/uDH1Ih2aNn4s6VItTQIclpHTudntgGIrnf9aCfR7H7DKaLNxjZieYhFCgY2jnYXPq85f0NKLCO2VcQgTkiTGMWe+rL9PuwlBPZeItkSV0Vg+6LXaX3Mj2jb2+dGtVPbCW1P/0UhHtX27Rdbj9cp8+P7yqS+x+orio1+TS6P3YlsYBDKtQc/pgjt2LLB2EZCgyDdTCND+XQAJDC2jIxeBfuIvZ40+DE0A6QrtGcIb98fkSGN3ziziBn0GLuJuqn73GXfgMeSKLZpT/Jh1xbYe84o4rI1gb2UeCu1hoTKQkJ2jqBOJVVwp5Snvoexh5Ravzao0FaU7bPXy2eXItsmVWxL23w+bXvdFdqxZTfbiMHOHmKi2XKdcWaQk8B2sozIE9SMfdliNDvCaUKaQkJ7ShdJKDf2pG7kxitFtIGxVcRgBjwOfUuPYk8j2X4hnCuwpYwk0jFaS8TvgS0K7Nh+JYI7RRiWlqVsc+vM+ZfSdmrfUt/vkvez5DjTOucR2oriQ78ycfb4HkVFNhG9hYgeJqL7rLInENHdRHR///r4vvw2IvotIvpI//pXPW3+OBH9MRF9sP/30pTOMlgc+Aj4xbZve4nQdutIywYTpTbRbPF8nLzZ43J7PW4Z8Q2MHLXROrM6hqLbroAryYcd2Z4qrif7tQzXj+0K7NOrYxWZ+qghPvDEMFFsnxBuRaEdF9juPu5yirje0jULXK7AtimJvOaWpQjvmlHtlDZrR7ClshKhXSbG1xHaW7teFUWpR0ok+04AL3HKXg/gHma+GcA9/ToAPALgbzLzXwLwagA/H2j3p5n5lv7fe/K6PUSkY9Osp2YZ8ZXZQjvFn+1mGzGMrCHCBDSAEchjsX3Kfx2xjJhjjNrrxbdP5Hf7H0/e7CVxW5cEdstyZpHTeuRm6hPatlXE4Kbty4liT7OSTKPMbnmJwPa169YTuBMbuWavisB2t5cKwdSIdq6onhO5ltrwbUspLxHFNR5gNiy078RGrldlHSo9F18J9vZeRUU2M78fwGed4pcBuKtfvgvAy/u6H2DmB/vyjwL4CiJ6TJ2u+iOjqWLb3uaWSwMiYwMkfbYRYDwI0hcpdWeBPO0rDIAE/JYRabktEM2ubzs4Ac0MX7Z0Q0rNUx37SdkV2K5VxDfgMRcTxU4bqFgmsA1u9Do28HFL16zEpQtsd72W4A6Vu9tLIts5+/q2h/odq3eu9zq03pWdV2hv/XpVFKWcUk/2k5n5IQDoX28Q6nw3gA8w8xc9bbyOiD7c/1T2+NQD+wY9dttksS1t92UZseu6+/v82VI028UeBOkObDy1LwyAPO3vsYxMl6fiazT4MTa9uivObTFdKKxD9xiTIzsXKYo9iWQLVhH7uO7ppEax3SnrXZvIOBKdJrB9XuwccR1htWvWZq7ATm1zKwLbXS+pEyq3t6W+X7mkCu7Ssti6XebacmoI6y0IbYFNXK/K8ix02V40e3rPFhn4SETfDOCNAH7AU+VnATwTwC0AHgLwU4G2bieie4no3i84qqh2lhF7fVqvj4TCv903CDKYXaSd2kfs9ZhlRPJln9Yjgx9PafymHfPuk4pPN9vlPnEtZRY59jfX2E3YFdo+q4h9LGkwYwxJ8Eo+bCBNYEv7+dozbdacMKjWNWtfr//vn4yDczUE9lIC6RwC211PO5e4XcSHLzId+xciVG+OsPY9MPv2qfH+h9a7stWFtpel7rGffuSRan1UFKVcZH+KiG4EgP71YbOBiJ4K4B0A/i4z/560MzN/ipmPzNwCeBOAF/gOxMx3MPOtzHzrddR4B8vFBj6aOtK2kNCWtrv+7FBkOwdpAKTBZxkBpr5sN9IaRciVba/TzFzZqZj0fdF6bRu8SZrlkFVEGvA4N4rtrkvTrM8V2DPE9VmuWft6/cqvfcKpvIbwSInUSnmwY+2sIbDd9doR7TlR7VThHepjrKxGBPocQttlrtDOYJV77JOuv35uvxXlLFR8Zl2UUpH9LnSDLtC/vhMAiOhxAN4N4EeY+Vd9O5s/Hj2vAHCfr66Eb9Bjt20qpmN+bLvc58cO+bOH405FvevNlgZASpObGEKWEbvMXXbba01UO2gVSRBvmYLbnh+SrWVXC5U8mJjotr3utuezithIgxlDGCHtiuKQD9vsZ7+6bZp2pIGTblu+dgKsds3mCuxy4TZ/opm1hV2uuK4hqlOoFcHe3+cR/07llGWw6j32qrGWXtuLUFTKSUnh91YAvwbgWUT0ABG9BsAbANxGRPcDuK1fB4DXAfgGAP+llTrohr6dNxPRrX29n+xTEH0YwLcD+PulJxAS2249e1tsUGNoHYjbRnJFY8wyIu8TnoTGO/MjMKTxC/ZpmTzMrk3E6693Mov4bvRSFBtIt4qM+haJYksR/1SbiIsrulOj1zFv9pau2asqsEssECXi2od0zeT8C1FDbNdcT5lZM8TaQntL16uiKHW5FqvAzK/ybHqxUPcfAfhHnna+z1r+3tQOjtvoBNlBmMPeiNoDkVWGvkyuY9o6MnvL5DrdcgsAbLc/7duR0T+utmj6Z5q2X27RP+UcrHM8MloAh2ZYx4G6yOjhgPbIOPTrdGhOUepD0+1gBjhSk/gjxfE4/ha0RwBfNq3H7bijmfieOabR/7SoXEjE+Pb3WUXsAY8pSCJXimLb5bHXmFCXtnn7t5Frlj3xoUsT2EvYFHIFW+1IttveoZn+0TV13G3HlqNltdcfbRnXPNtj+0pM9xn+xuacZ8rxtnK9KsreaBmIXMqrs8sZH+dkGDF13G3pgyHl+nOi2fYASINkGYn5sn2T0Jz+efyqIcGYRKFnW0p7mN2GILbttnyvALwDHlO82F09KbVe3CZSIrBjwn4v1BbYKW1dssBOiTyf6lo2u5DlLnSc2hHsmu9lyN9f43NIjWinHF9R9CtxNdilyLZJFds5GUb8x5qKbtc2IvfF7812cS0j7nLMl222+UX3UbaK+ARbSEBXnAVS+oMjZRaRBj0CjvDx+LFdq8ioXy3DzaE96bvgxbbLT+uCTSQ04NGtY7ch1Z2Zym9zzBGasQwQexLYOWI1JK5zxXR2/UyxnVNnrvD2jdEoWZcoGVib076iKJfF7kR2TnYRqX7dgY/T/e1tKdFsaQZIO8tI60SrXSQvdioToWa3H7qZeMS1uYewsy5hvy9uBLtlf3q/0/5teBprV1i7E9DYx+bIsSTcKHZX5reJ+MpaqV5EYO+Vc082szeB7a6nlJ22ZUamU4i1GRLbsXo563PE8TK/NJSl9lMUpT5bv9R2J7KB8B//Oan83LIU2wiQFs1OwZdlxI14u/myu7JwTmz/MdP3Cc4AGTqGSX2YsHvuxDShyJdsEbH6NXm/wwMec6LYZpv96pIjsPduF1ljspkccgR2bN+cSG3K/qHjpwrrtv8u+/7FCP7NzYjAl67n1N1yDm1FUa4WuxTZNjVT+cXK3G3TZanuILxTLCNSVBvw+7IBX4T7OMowMkrj5xIYaNcfYFo2g1EUe7Tsqd/Gsx9I4trlJLqdQY4lKfxSotj2ss+HnSqw3ePvXWD7WOon+5zoZ24WkTl1UwS4+H0PiOsSEZ2zT0hsx8ouSWi7qNBWUtGvxdVh9yLbUJrKzy33RaFzotlmW/rAx+k06+OJaMYR7Vjqvmh0OlWknVHI+X5RCPkbQzdCnx87xSrii2JP68Wj2PayNNAxdV/f+tbZWyaRcwrs0Lq3zPN3LkdQpxJrUxxkXjmC7a4v9bBUtl6e2k9RlKvBrkQ2YxqhdinNLiLVT/FjTzOLBAQjh6dadyemaUMniungx5KZHqPLCxK8eSd2YRINtN57V1inWkV8GFGdG8UOtQekCew92kW8aRsLBXZKWzUjlGsJbFGoRsR1CubhUfoXIyS4U6LaUtQ+Vt+3nrNtbg5tFxXaiqLksCuRbRNK49dtzxfaKf7sUH1fNNvXx5BlZKjjRLFbk13EqhOY6dFO4RdjLdFWY7CWFMX2IU1Ak8vcKHauwJaOv0fmCOxzDnRcQ4z7jlMirnOFdE596dglUe1c4R3aliO0U9uJ9WGoc56ghKIoMlt+ht2tyLYpySwibbfLUsX7cPx4NDuEaxlJ8WUDUz+2EdStmL5PiHYvLNbM22AuAnPT8kWMpZuam77v2A4p/Xz7evNkO5FuOaItD3iUxW48ih3yYafua6+rwK4fkSwVYksKbEm4hsR1TmQ6hVh7c6LavvVaVpE5D1Bl1h4dCKkoypSLENmGEqEtledkF4lFs+36rmVEwpcnW2KadSQtojIZ3CgNduyF3CmjSOXBj6dDC+/7aV0Q0pP9A1HpmB/bJmYVGfYTbBuJfmqXUD5taf+9imtgnsBYc6DjmgLbJSauUykR4776OVHt1PU1RHhNm1FOHUVRLptdiWyG/AfcxpfCLzbg0S0P4c/VHY9y29hZRkblthh08mVLgx+7fWb4sUfldYRcbiq+Ofu7YjzXLlIS+QtPqx6PYktZXHIF9p5FN5AW7Vt7oGPJttoC2xe9jgnlFP91rkc7JLZdcoV2at3Szyh3IGSMUn+2oihXh12JbJvoRAmRqPbcSWlCy2Y9xzIS8mXH95Wm/G5HafxEMqKuwz7LRLTtm3SpQE8d9Og7rl2WahUpjWLn1Nu7ZWSOTSRWp2YEslYEtbQ/PnuIS0gI17KMxNqRtvmi2qP1BSLRc/zZcz47eR8V2oqiDOxWZNvkCG3f9lwPtS9XNuC3jMRws4mcoteewY92HYN/OvWC7COVOfmz+27kvOcmWu3+y+5DIOIdH/DlT+UXWvZFsVNsInu3jFyKD9u3rZZlJMUekit6axE7rstSQrvWg07NgZAp31tFUa4uFyGyAb+NJGf2R7esJJodsoyk+LJ9EWw55Z8b/Y7/cZ+Kcr8fOyjoKnq07fuUe8+KiWl3m+S79g16HPbJi553kWT/+5grhC9VYM9hLz7skjYmdRPsIXPEdWy2x9Qc275jrSm0S9oI7VdjPeUYiqJcDS5GZBtKhHasPOdY7nFjdYwv2yY0+FHKMNLVSxe93ro+ETdTUJfunXpjcuvFxII0OLIE11ctieCUKLa0/6V6srfgw07pk7RtCctIqj1EKgtl/SidnCZlv5C3223LJia0S7Yt5c/ORf3ZSir6Nbha7E5kx/Jjd3XyhHbphDShY+YKy9Dgxxhr20BqMWewpC+iPfVmTyPdoz60sh9bmqWxay+vvKTeVRLYKfvNXU9N57a0ZWSOwJY494yPKX3LEdrn/iw0f7ayBg2t3QPlnERFNhG9hYgeJqL7rLInENHdRHR///p4a9uPENEniOjjRPQdnja9++eQMxmNqR9vMzF6yvJyThsuPquIL8NIaB+TK9srwEdR0/PfDOJ++fz3cK7AiGclyfNku2WlUexQXYktXrOX7MNOrRfaL0Vg56TRq81aQju1Xo3o9hK/lqQI7S1er4qi1CElkn0ngJc4Za8HcA8z3wzgnn4dRPRNAF4J4Jv7ff4JER2ENsX9SykV2qXR7NAxfHV8vmyXNkFAh2iF2R1zrCRL40arU8WBNBGNdFOTBjYat0ts0GMqqQ8lvuj30E5ZZpEE7sTGr1mJS/NhB/tpXQcpAxxLxTUzZ//zkZNKMFdoj7adMbq9dFq/RO7EDq9XRVHiREU2M78fwGed4pcBuKtfvgvAy63ytzHzF5n59wF8AsALhGZ9+xeTI7Rj20v28bcVbCp58KObYaRbTs+VXUVoLzQhDTD2qbldLY1M+XCFRIlNJeTHFiPVBVHs0oGPW7tmt2ITqb2tWOQFvm+lAwtH9RMEc4g5Yju0HhLa537IsQn9uhFrp4ZtZGvXq6Io9Sj1ZD+ZmR8CgP71hr786wD8kVXvgb4sdf8JRHQ7Ed1LRPf+OcIiI1Vop8z6mELIMgKk+7JDEev0WRzj9aaiXMos0vq3ZTJzPppkJn7srEwhoW3hfNRzBieu4LM+yzVrX69f+JPPqU3ErZf5S06OwJ4jrEvaqyG0bc76OWzQNuKwyj320488kttPRVEC1B74KFn6Z/3VZ+Y7mPlWZr71sZB+FRtTEtEORbNTLCO5x5MIZRiR65dFlbMzi+S27zltLvwapEaZfO+3m74vllnEHvQ4tBGakEZ+32JWkdj+Z8wuUvWata/X6742zQa6pk0kdJzq9SICO0WgisK2srjOaX+u0F7Cn11Sb+lsIxVZ9B77pOuvn9OUoigOpSL7U0R0IwD0rw/35Q8AuMmq91QAD2bsH4SRFh1OG+BYvm9XL3CjKPyT5xPWw1TqnhvdhjzXcykdNOpSMhAsZZ/Yw02uVSSFSgL77Nes9FFuzSaylqgrEdgSKeLaN3V6znTq5ljS8UqEtk2pP7t2vY1lG1nlHqsoSl1KRfa7ALy6X341gHda5a8koscQ0TMA3AzgNzL2T6JFXGynDFJcglI/dw5ujuwlcb3H5yQ3GpQzeDF1sg/xOAn5sXPL50xmk8iq1yxwHpuIy1o2kdyBjqH1EoFdOr16yn6lQjtUP+TPHtVL/Fx8+8zZVvNhL4HVr1dF2QtbTouYksLvrQB+DcCziOgBInoNgDcAuI2I7gdwW78OZv4ogF8C8NsA3gvgtcx87Nt5MxHd2jcr7p9LidD2bc+xjJRgMoqY9nxtjQY2JvyRLhHco2jsirlc29P7u+xDw1LTTc9lqRzZW75mbZawiaw5oNG7T8ZAxxSBHbJv1JxevYbQDrWX6s+u8ZDj28dlDdvIXq5XRVHyuRarwMyv8mx6saf+TwD4CaH8+6zlz/j2z6VFXjj+yIwD1XvsOTJwoOmyr45bvrvZgDbOyHPNYQETKw8R8kyn+rFLSBLmG7xma9hEcvdPjWKvaROxSRXYKfvWwrRLQqiImUHO39K2ZTRWXW55tK+7btcP/W0+toyDqWcth0jdJ7U9qW5sPYUtXq+KotThIjRe7VhsTgQ8RqxvS0wiwW2XK3urM0HO+kWg9efI3itnsIqsSqVsC9UGO5ZGOYvay7CJxKglsEsmr/E+oCZEtEv92dU/i8R6ubmzF7aNKBfIlu0NSl0uQmSHqCmY849d1rhkAUktc1nTUz2HkshnKvV+Tk+IKjuDHnNE9CUKbkAW2Occ7FiyrUY2EZtcm0ipwLanRnfFdWib71hiRp4CoR2qazP7Myisl5M7OwUV2opyNbkYkV0jZpsriqtlwqiYHWRLszvmErsRLXGjKpmIxsfSAnqPonvJhyUfSw92LNlnjk2kRGCXTrWeKrYnZTNTltqk/l3d0yBIRVGWYeu/ClyMyM5hiYF2Sw3ec9P2XVK6vhoseTPj9riov/oqstXBjqn9KRnsWCuqm9JGqbjObSdFaOfYRmoMgizZJ8c2MhcV3opy9bgoke27fZ8x492qx1TqMdcnfVUi1XNZa7BjaNuS4jvHnwzIEeKQwK7N0kLbV1ej2cqls/UIrFKHixLZS5A706NytbiKwriUpQc7xvb1bavuyw5EsW1KbCLnFNh2295c3TOPm7r/VqLZcx8CFUWpxx4eVFRkK0oCKqbncY7BjqVR7JJ6vn1yBjvanEtg58zwWHqcrUaza2eYkeqqqFYUxUZF9s5oDuGPjJztdDgs2Z2q5OaXLd2nBGr28z7ugaXFyFpRbJtcq0WIOQI7JKpzRXfqzI4xoR3b3+BL6Vf7oemcKf0URbk6qMiOYCZHkCaTCe9X5/gUaKjxbKNm/x+rJJ7PJahzUPEd5xyDHS89ip2yn3TM0mnVc49b66HB136MNaPZyv5Z686ywVvabtjLe7d/NXZF8AlqH3RovGJ7bRFea8bNJUW3LZ5VSNdFo9jzBWms/XN5pYNtVIpm22g0W1GUPaEiuxJzhKNrAckV1LOICO6t2U0ODZ3+1aAJfG7UHNAUCuwSYX6JYl6j2POi2CUCuxa50ealotlbzDSiKLXYS0R2S+zpPbsoke07GVezVoukRtqpdZxLpTlZcc77PtGertALYytR7NQ2Svp7LhF8jrbnCu0tRrOXyjSi0WxFUVwuSmTPZQ1R3MwUfNWi3ilRVNr+18V+P+ns4j09En2JUWsXRlxUrBXFXisvtk3NKPbexHtK2xrNVq4KGvdJZ2/v1fZVUyKlJ7K0MyPUL+nY9kBHX8R1jrB2s49MG2/6Y68vAmtZQsz76Hs/SyPbKe+Ra7eZ875u4TOZw6VGsUvzYueyZC7sGDnZTc4RzbaZa/XJ2TY3mq0oytXiYkS2jxI9GtvHtz1UbkfJ3fUYRnj7Mo3E0vp5260l2hIi3JQ4fnvOrwk5YnnuLwi5qEd7yhai2KmU7FM7il1ynJosdZxkm4gnnV9wnwo2ERXKyjnYW4R2Dfb4Hl2bszMR/RCA70eXAedNzPzfEdE/A/CsvsrjAPwrZr5F2PcPAPwZgCOAR5n51tJ+5EjMHBHn1pX2zRHxMXGdI5bdDCHRCHVina1xrSH8RcF+TUNZN0dqCMiqfxhNUGOvN80BbcbkNfa+brux4+ay1jW71Sj2bNtIoo1hqSh2aruxtIBzrFVty5OHVm559NDLzEXHkNqWOLZ8+uXLXk7dJ2fboy3jmrXNrRtbz2Er91hFUcooFtlE9Bx0F/8LAPwFgPcS0buZ+W9bdX4KwJ8Emvl2Zn6ktA9Avh3Dtz0kfvOEdKWsFwWCOJSar7rAruzPDt2DUm5QByK0ggfYFdtNQzgeZcHR1Y33lQ4H8PE8M0DOFdWjtjZyzQLbj2LXHvAYYk4Uu6T9UJ2YEHbFcykh8Zx6jBLxWip45wjlUrZ0vSrnITPWc6XYYxQbmGcXeTaAX2fmLzDzowDeB+AVZiN1f63/FoC3zuuiTIP8ztcc2Di2f7gR7/z2/P5rN2JtebYF4Typ3zSywB7lgY68k4WCWnq7QynzDFJ3D4E+ujc/SShIx5Xe89h7IW332Tpido9SO8gMG8kq1+yaUewa+y094LGUFDGeOrFNaX3D3HPa+gBIl9BD3ty2LVa9xyrKVtirwAbmiez7ALyIiJ5IRNcBeCmAm6ztLwTwKWa+37M/A/gVIvotIro99aCp4rp0bGCpH3taL99z7VsH8iaQoUMnrLOj4Wf0AJtTzPFGu/mxS/Nl2yJcen6g5jD611jL0baFOmbwo9km1glMfhOrn8Eq16zL3MFhOQJn0TzZK1tFosctFMyx/ZItKhsdALnErI8LDXjcxPWqnJc9C8ol2Pv7UWwXYeaPEdEbAdwN4PMAPgTgUavKqxB+wv4rzPwgEd0A4G4i+h1mfr9bqf/jcDsAfBXShIUkhEPRZtlrTaN6MT+2dMwUiRsSwr6BjuNodoHIjGYY8YvBcxF6SLnWEI4ez7XtraaGwEcGNQC3/XrlqKrPzpHqy65pB4lxjmvWvl6/+kk3VhlkOEfslLRTe4bHUL1Sq0isXqnAtvfP9VCn+qfncmQ+/X2o4b9Oreduc73ZKW3nsMY99qabbnI3KyugtpHLYZaxlpl/jpmfx8wvAvBZAPcDABFdA/BdAP5ZYN8H+9eHAbwDne9MqncHM9/KzLc+NkFkz0nJNzedn0+IH4gmov5AchRXSs9nynyCPCfKPbWTZArpmJ1ixnuYYiUJ7p9xw7OtIqXHnRNxXiuavfQ1a1+v133t4ydtzI3wxVKo1dg2d5+aD3IlUey5AjvpGJWi2altlrwP586TvUQ0+9z32Cddf/3sPitKLfYexQZmiuz+CRlE9DR0F7x5qv5rAH6HmR/w7PeVRPTVZhnAX0f309gs/Cn0yqLY/uOU+bFdse2SkiPb4IrxpOwiGWL8nPhONccKMvFlZ+bEpoayBnSF8l+nWEZKqPHLwjmv2RStVzPP8FkzjJzJKnKuNsXjnEGsb8EyskT7tdjaPVY5H5cgMOdwKec/K4UfgLcT0RMBfAnAa5n5c335K+H8jEVETwHwZmZ+KYAnA3hH/3PkNQC/yMzvndOREoGd2qZrHYnvl//t8EapnRzZtriWhLZPSMcHPy5nDWnQ5ZBKquu8dUmZRQIZRLrvWJ+twMkqIqX5i2UYMe8Tt+2obFZaPU8Kv4WsJKtds7UFyjkHPIbYUlaRcwjjEOeyjNic0zLikpvOr4DN3GMvne5OsS2uqm3kUgQ2MFNkM/MLPeX/oVD2ILqBG2DmTwL4ljnHNsQix+F97Yh0+XFL/dhAJ57dCGrOgEWprhHbdDh0AyAl4e2LavvEdoWUfebtbhoAbff+fynhz5pvgKMp94khX67skQgXfNrSg0rf5ajolfJlmzKT+u+0niCiQ/m4S9jCNWuombYv1va56tW0PKw5w6Mh5M2ulc6vpE3blx2st4AX+5xs6XpV1uGqCe1LEtjAjmd87LzOoe2xgYqywPYNeJQGQIZsI0Mf5U42DXkEsh2pNlOcN6NtJRPRBDkIwtpEbCumPQxhR798HmkjqkNZRaQbtGnb127p8wMdDl6bSO4vAzl+7D3OBLnVyWiK6m3UKrJ2FNtHji87ROpDx9Je7DkPf4pSwqUJTx+XeJ67E9kxcd3VCQvsnP18fcgtN37skC/btn/Esoa4wjovxd/2RVrJYET784tlRnC35x4v9f1uIgMfS0V6akrBrTJXdO/dKqIM1PBlL+3FzmGhdH7KFecSBajNpZ7f7kR2jBSBHbOJpESxQ22XvKm+QY9uZpFQ+r6YzUT0bJ/Jl+0jNAg19SdaN7JNwrKJVkvb7HVqKOgp9Ynb6MBHI6qFB5zS/NuXxBpWkTVZepbHmuRGns/14FEyMU1pvT18p5TL52KF6IWeF3BBIruLEJcL7NzBiilWkRTIYxsB/NHsUcRbsI6YiWjMbI/m37Qhny878WsR8FnEIsOpkeNDQ95ctJJtpAmIaKncJ6ipacRJaSb1EiwjsWi2r+wSbCLAdq0iW/Zj74U9Z08BlrOMaDRbWYpLE6SXdj4uuxfZPnHdbZvWjbc3rhvKMOIuTzOZjC0idn7s5tCIMz2GfNpSDu1ue/7HOBFs4uDIg6kMoMyffRrsaN5HaQCj/cASFNTNSVhLwtvr0yYTzZbFdRfBDp+H2K77gFMpmh0T2nsV24ZcAZKTG7tWn7z1zuR7zhXlW/Vj16a2L1tR9sglCNOGLuM8YuxWZMfEdUxghwY7phzb127pG+oKaHfQo8Gsl+TJthov6OGoE/P2j1CSAtEX0Z68BnzbDaXlypaEbmo02xXaKeK64rTqZ2fJSV9y9z2nH3vvEd7azBn8eE5ftlpGlL2wZ5G6136XsCuRTQiLa2DZKdVDUWy3/VSh6Itou0hl09kbPbaQUTuRfNlnHBRpR5Onfuz0dlInopG2S3WNLzvHMiIfJ+29LPVk70Vo2+wtV7ZyHkrtNLV92VnHVsuIsgH2JFj3/GBQyq5Edghf1pFUgR0a3OhrLzWFn88q4hN4Bt+gR1soS6LZzZFtBjyKVpS5vuwC0rO4+FP1AbInW8ow4g5+tMsA9IK6wArTHIKWEbfMF8327X8pnuwQuQMea80Aec42XK6KtWMvaPRaMexV/21dvG69f0uye5EdSumXK7ClujlR7MbTVgquH9ud6fF0DKHcJ6Cjx0zxZS9sDbHtG6Hp1aV/Uj3DIKz714gvu9uWNiCzkewingGQ0VR8GbYRs36JYrsGiw+ADIjjOVaOPdtAlqLGe7Kmd19R1mBrYnZr/VmD3YrsmLguEdi1JqIJ5cJ26cS17Mcel0lRbzmzSBITgR1J5VdBbKdcbEX5sR3RHZvWOeTLBsap/CTLyLS+HM1O8WZL+0nLlxDV3opV5NxcamaRtajxftaKXtf85UVRarG2uF37+FtiVyK782TniWsgT2DHCEWx5f74rSJTTzVNItSAFdUWBj1KotpO3zduv7ORuBHrLMFWILYlIWu/364o7i7Q+OdxTbKLCGLbfQWmvuyYMJdwxa8bzbbr2a8h28ilz/xokytAallF1B6wPGs9WGj0WlEGjNg9h+A957H2xK5Eto+QuM4V2HOi2DkDHm0kq0jMj904vmyftzqYJxvAZEr1tQZBCm9bQ1NriJ3Gz0W0iyT6ss16yjOENAAyJZrtawsoF9qXxJ6mqz53ZhFlPvpwpVxlbBFcQwjXbu9S2bXILs2RXSqwU6PYsenTDTGriG8yGmkApLQeZWHBJl14dpF7eqFoshS1PrXjCnHBfw34fdm+VH4+y8jknDzR7JBHO5al5NJ82WtOSFO6356El/Rr0SURenA5V+7y0/HUEqJcAK5Izv2npLE7kW2EdWmO7NLsIvGItj8dYIpVBJgOZjQMUe1p+1IebZNZxAc1U8tIf4BxnR5eePCjTfbMmwG7iEHKHOLaUXItIyaaPRbDzWi7uxyzjQBhoX1JUe25wuTcWUaUPErsV0uwhm1IfdmKohh2J7J9+MR1jsB225vWm0a0fVHsVIxVRErdZ7YDUz/2WITLdhA3fR8dGm/0OluwBYS3dPb2W9J4HlROZU0kF7onw0iKH3s606NsGXEnpsmNZrvlvvc3R2iH2tk7OoBsu1x6lFxRbPTbrtRk9yK7Vn5suzzFJhKLYscGPPqsInY0O+bHdr3WdChL5TeJattCbmxizm87Ae9A1ganXNmx1H1j3/bYFiL5smOWEUMswp0SzY6l9isR2nsS2+cWyEtEL5dK35dDSS53pQ76kKcoSgmzVBMR/RAR3UdEHyWiH+7LfpyI/piIPtj/e6ln35cQ0ceJ6BNE9Pqc4xph7RPX50rf5+bFLh74KGQVMeuSRQQY+69ly0j8o6VGiGxXnoSm8cQF3MOUvG9A59UetdOYz20aoQbGUblSy4gU0ZYyjZhyu4706rbttiG179s/2veVrtklUQHUcZUizqGBp+ewiCw5iZLNJV6vinKVuFa6IxE9B8D3A3gBgL8A8F4iene/+aeZ+b8N7HsA8DMAbgPwAIDfJKJ3MfNvh48ZTt83LfPXCQlsX9s+m0gsii3RHGiSVcSUG8ZRbZqUjaKmosd7yCwySt+3UiSUQACGm00ncof1AxFait+MugwjjENDp5uXiWYf23E5NQQ4N7jG3Q6M6nRljKYltP3b2gBo+0+d26NV99Bt68vM+8ptCzocwMehnNuj97VpDqM2zDHsNtxtuaxxzUqc04+tzCMm3DW6vhxbuV4VRSlnTtjy2QB+nZm/wMyPAngfgFck7vsCAJ9g5k8y818AeBuAl5V0whe5niOwc2wi42P6BPXUKuKrY68bYn5su15x2j1hX7bPx2MVWWJQZEN0ypVtp/HzZRiRrCJAzI/tHDNgGZGIRZZDtpHYQMhJW4dDNKqdyCauWZcl/dhXTZBfpWj20mzgu7PJ61VRlHTmKKT7ALyIiJ5IRNcBeCmAm/ptryOiDxPRW4jo8cK+Xwfgj6z1B/qyKHZ2kdTo9RyB7bOJjNsfHz91xkcz4NEV3SREsyU/9lBnmsqvybF9SIItJOJmCGv3I5uThcDnxbaXJV+2veyzjLgDIN10fuN9DkGB7Ja5+9qvjdWWz4IiHSeRs1+zGxAqXraSvm+r0eCrINg3nqVmlXusooMflXoUqyVm/hiANwK4G8B7AXwIwKMAfhbAMwHcAuAhAD8l7C59h8W/YER0OxHdS0T3foFbb39SotelAluyibiRa0lYhwY8ytFsgj3Lo5u6zxXcsUGPdmYR4WCAZ4bCiWF6ZrTa1RBuNLqhvPR5scwiri+bHMENxLOMpOCKYN8gyNRsI9JgSLfcjWrncI5r1r5e//xPP1fUzzlsWdTn4LseUr6nNcTxVRDY5yb3u7nGPfbTjzyS1UdFUcLMUk/M/HPM/DxmfhGAzwK4n5k/xcxHZm4BvAndz1YuD2B4IgeApwJ40HOMO5j5Vma+9TpH7PkGQMai1yUCO2QTmR5bOhOZUwq/TKuI/RoaBDkcx/JiB6LctbzaJffohjpx4U3r5xHX1ySBnZTCbyq8ieyo9VSIh6LZ9vIgptNtI+6yT2gD06h2Kktfs/b1+tivmQbYLkUEb505Ijl1X5/g30qObMNS37ncwY8lnPse+6Trr5/dZ0VRBuZmF7mhf30agO8C8FYiutGq8gp0P3m5/CaAm4noGUT05QBeCeBdKcfMySzii16bbW55TGD7BjuWRLHd3NiAEcx+q4iLJMZN/ezZH7sGp2XOg02pB3uaTzx8Iza5sk0aP18dad03M6RkGQGmObFH+zTTLCTDtmmWkVTbiPQaSu/n1rHbzGGNazaETkqTT+qvLiVCe6kI9lYtMS5b+45s7XpVFCWP4uwiPW8noicC+BKA1zLz54jo54noFnQ/Tf0BgB8AACJ6CoA3M/NLmflRInodgF8GcADwFmb+aOxgvj/TNTOLxAS2bRPxWUZyIzluzmzJKtIth/3YE8+ulVkkePzmEPZgL4TJJvKl3P0awqFpcOyzbPgyixwawvHIoIZOuYztbCN2lhGzrcsUgj6dyPiGa4SCyTTCbWttM1lFptlEuvIh24gvw4i7nykzQlvKPlLA2a7ZktmuY4MetyaCto4RzZzwYeQN/N2HaL4AznqPVRSlLrNENjO/UCj7Xk/dB9EN3DDr7wHwntJjx6Y/99VLHeRoYwtsuZ3pvilRbDeF32S9GW/rXmNCWx706KbvO+XIDgnwaQoOf110do9j4F7u254itu0MI7bQmohqZ/lAhBbsFdfdKcodaxpCJ6P7dH6CUJHEtUnpNxbPTZHQttt20/yVsOY1q3QQUZLobRoK5oPOPSYwFdvqvd42er2uB8FjYleUDHY14yMhnFUkdeCj5MuWIt0HoonAtq0hUmYRYxPJwR7weFq3RHXIjz3sIw96LIGa8sF1o3aEslAAzHwuQ/q+IY3fpK7jz071ZccsI7EJaVxv9lAet424AyFTvdluu02hwF6bLc38uDVyI8OlkWQiGv0raiNw7K35seeyp++QoijbY1ci26V04KNbXlYW9mSnRrFD6ftCVpHR1OqeQZCmXpY/2yPgWLohF/qz59yGkzOLOK/uIEZD06fqm/TRGQDp82a7gyBtsW1nG6khtC9FbG+RJcXUUsJzL5YNqZ9rRtDPmXe9xuBHRVH2y+5Edu2Bj6EyaaBjyCZiD3bMwQx4zLWK+PzY4sBHO7OInb6vLzvZSSrju5f6BhP6OJAkrpskge2m8gMAKXuIHc324Yt4S9Osu8s5QltadtvdO5cSJZwOYK4nILcWGd6LsD8XOmZAUZQQuxPZLtLENJK4Hg9WHMp9Zb6BjkN7dvvTm2FqFLtxBHmuVSQ2KU0VFpjVEej1vidHthHVJsPIZLsjrr0CO2AZAbqImnR8KZ2f9DaEbCP2JDW+/Ng+oR1bviSxbZgb9buKAuecojd2rDkPBFt7mFAURanBbkV2ynTqpbM9hgY6hmwi9mDHHORc2WlWEXsdABohb3ZxlJqaKtOmpwStjdhuhAcWG19ebGDwZadaRqSc2aF0fqaeFPGWbCOncxMF9PRXiFzLyCUKbZuYaN6zqJbsEqV5py8xurykoFeUVPRbpsxlVyKbKE1cd2VyZDs2GU1soOPQ3tQmYpMaxXYHJ5JV5ka1xdecSWnszCIhmoPswbaIbXeZ68FsRLuI3yoyKbcsI5PZHj2CJzQ5jVtvWJetHtJU6TGhHbKM7E1g1xDEexbVS7O00C4VvbX82Jf4IKEoyuWzK5HtUmvQY0hgu/u69pGRwLIGO+YgWUckwTwV5GNvr7tfcNCj8WKffNnx2SDnkntvtTOM2LiDHyWBLS2PPisnYm0GQJpotvccrEGQ0/2nszvay76MIz6PdmhZWle2y9zIa8r+SwjR2BgFRVEUxc/uRHZORpGcQY8+gS15st1lX5aQlCj2ZL/G8mFbgyF9UerYBDV9pXqCrFOi3s2xLxSBul8kGt8vEkMaP4mpF7sRy31lrmgIRailaLav3rDewBeN7o4nz+woCe2UqLayX3IsI8ltVhTEqW3lRLEVRVGuErsT2TY1Bj02CAtsCNvMsmsTsQc75mALcoMvqh0S3U0zFtoTW4jJLFLKAgMgzfsZn2Z9XCfXl22OZfANgDTRbIlQSj/JNuIu+4S2L+uIrx13vz2yNeuHazOayxICMzUaXiP6PFdge9sVrvNL91drGr99c9nfTmVpdieyJWHdlecPehyn6BtvC3myAdkmYpMaxZ56uclrFfH5sUdljrgWJ5Wx0/elslCGkRhixDtiC5FebctIaACkwU3VJ0cdw7YRKZIdT/M3CO1YVFu5TGpN9pIrtk39GgJ7jsjXCLiiKJfCrkS29Kc3RVzH/Nc5Atv2YU8zgjRiVDqGqe/mxg5FrVP82MNKIIJtZx8xAyMPh8EWErGHiE1WmGiiEcS1O/gxVWBL9X0DIH3R7NggSMk2MixPhbY8ENI/INLe7u6n1GcygNb9LgqffwzRblRwrWRHjy3xHPp3Vaj9q4WiKIqPXYlsg+TLzvFkyyn6pgLbtw0YC2yfTSQlij31cjeiVaQrD6fyCy13/UzILFKJkvuYncZP2mYzjlKPfdmSZcTOMhIaAOkeMyRAYrYR15/tvjaNP4+2OyBSimorl8vWRW9JFLvUKrL198Jla1YoZT77+gYqW2JXIptQNuAx5r/2CWxp0KPPh21wbSIx7Ci2mxtbyioipe7r+uUR15IoWziLyOkwJjuI8CeKzPYG3glp7DYM9syPki87J5ItDYB0o9mSbUTKsW3bRnKEdnfskKXEH9Xei9hOER2X6FtNFYe+aHYt20ht1vZQu8cP2cmkdUVRlHOxK5FtyB3wCMT917kC2/VhS7M3DuV5UWw7N7YdtfZZRcRp1qVBj27fcn3ZM+jEdv+acM+TMozYzw45VhF3RkhpAGT2BEKCbUTyZw/184V2LKqt7I+aArVp/A+nS1E6MU6qLWZvUWtFUZQQuxPZuQMe3eh12H8dFtgGyYdtb3NtIj58UWxAjl7by65VxI5wN7YIb8ZRbUgC7Qw5slPxZRoZPVCJAjtsGXGXJV91TjTbxp1y3Y6SuwMhQ6/yzJD+qLaK7W0xa7BfQTTbcA6hnSLoc89/7Yi4ouSg31alhPVVVQEpnmxbXJt93Hq+iLZPYEs+7NPxDn5RnRLFltqYZgoJW0W8fuycSUwSZntcCp+4HoljQWxnR7Id24gve4iPmG3EtDtXaMei2sq6lPqJSwYu1uhLKXPbnjPbq0a2FUXZM7Pu1kT0Q0R0HxF9lIh+uC/7b4jod4jow0T0DiJ6nGffPyCijxDRB4no3rTjxT3ZkriWBzOOy3zrMYEtZRNJmT7djWK7Vo/JzI2JVhGfuM72ZVMDLsgsUoKdxcXGvblLAvua5yYcnQVS8IGP8mAHotm+faR+ShlHUoR2SlS7RGyf+5q9JGK53OcSEqOpQnstO0qNKPbaDxNbRK9XRdk3xQqKiJ4D4PsBvADAtwD4TiK6GcDdAJ7DzM8F8LsAfiTQzLcz8y3MfGvu8XPFdcx/La37BLbB9WHbNhGJUBTb3n5ad8R2ilXEfu2WHbuBG9V2LSUCTAQ0veiuiJQDG8Akw4g0+NHsb7fllvksI9IAyNRotq++PUmN6bNvIGT3GhbaXZt182Svfc3ujZIBc1uIvM4V27n7h855ThQ7haUffNZEr1dF2T9zVNOzAfw6M3+BmR8F8D4Ar2DmX+nXAeDXATx1bidtcsS1qW9vc9tIEdgGssokH7ZNaLCjFMV20/b5ItuSkHaP27VhCbGEQZDJAyArCG0ztbqEm6rPvX+btyXFlz3eNs2xLd2gY9HsSX1nsGMtoe3aR+ztbp0MVrlmt8q5slDkWEbmRrPdY9j/5tbL7ZPvXFKj2CUPLBeWSUSv141xUd8u5SzMUUz3AXgRET2RiK4D8FIANzl1/mMA/6tnfwbwK0T0W0R0u+8gRHQ7Ed1LRPd+vj2OOh4T16HotSm3y3wC284kYgvsmE0kh2HA5Dhy3QiRbFtAB/3Y7qBH+3iCQDtNRLMQRGFxHUrNZYviVF+2zzIiDYBMiWZLgyBH20br4/3cOiGhHbOPzEjdt/g1a1+vf/6nnyvt5yIsIcDmRowlYt/B0mi5K6bnRry3ELWPsXPRffZ77KcfeaRKxxVF6bhWuiMzf4yI3ojup6vPA/gQAPN0DSL60X79FzxN/BVmfpCIbgBwNxH9DjO/XzjOHQDuAICnX/sKdp8KJI+2b7s0qUyuwDbYAttnEymJYnfHnIpt1ypiyqXXvuL4FcBpOnW7jiTYYtHqgmg2Ebo/+QJNAxyP47IDEVrmyXJDhGPf0KEhHFvGtf61Wx/KAYy2AUPO5tPNtwVap2PUEJpuE9B2/WvB4NZ9G/p6LcCmfw2hBcAtgxqgabu+U0N9mdmHQU0DbltQcwC3x9NnY5bdMiO0W6s8h3Ncs/b1esMzv3nV5Nf296Bam0Q4crhN81nHyuZQu73cY0frZESxU6nhx96T6F7jHvv85z3v8hLWVyZwK1OUCbN++2fmn2Pm5zHziwB8FsD9AEBErwbwnQD+DrN8R2LmB/vXhwG8A53vLJlYdpGQJ9tXliKwfT7s0bpnsKMPO4rtG/AIjK0iOX5scdCjffyFhXbINilZMOzP1b6xNs7nDUgR7MEykhLJNseQJpwZ+i8Pghztb5XZAyHdjCPmVYpoh/zZkle7hDWvWWVKSTT7VGcFwbiEwC61itTwY29ddOv1qij7Zm52kRv616cB+C4AbyWilwD4hwD+XWb+gme/rySirzbLAP46up/GoswR176UfUC+wJ4MUvTYREqj2K79I8UqEvJjRyenkR4IYkI64SEidAuTto389rbYHllEzKvfKjLUndpH7PXQTVbKpW33x/3pXvJnu/13hbZJ75dqH5EsJDmscc2eiyUEU0qbS3mMcwbiLk3qcZYa6JgSxa7x+W9NdF/y9aooV4Fiu0jP24noiQC+BOC1zPw5IvrHAB6D7ucpoBu48YNE9BQAb2bmlwJ4MoB39NuvAfhFZn5v6kHlfMr+Orn2EADJAluadCYlJ7bBF8Xu2p5Gtrt9hEi2axmR/NhSZhGbkoh2IQ0BRyv+ciBCSwzjyGgawvHIk7rGOtL0P9vnWEYATGwjpk00GI6NzgKCBqJtBBh+qj99T9BZQEzZYAnpflzkthParnWEW+4sJon2ka79obyAVa7ZvbCExSSG+fwliAieQOW4Xv89XMJCMnd6eKB+FPsKodfrBlHLiJLKLJHNzC8Uyr7BU/dBdAM3wMyfRJeSKAvCNCNErri2y0sF9qk/jg87ZBNJiWJ3bTbigEfRDuKzinj82P1JOx0br4sT0RQKbZ8PWxTYVkUjoN1th4bQHnnky7Y5nIR2g2N7HAlqrye753hM/5PZvR2EpsXJK+76s2sIbcDvz+6OWeTLPus1uyQ1BHFJG5IvOySUbXxe6hpC27QPzBfbNaPuOQI7lRSryCVEti/pelWUq8gyYcqFMTaP1GwiqfYQQBbYBnego6HUJuJGsSeRbDeVX4JV5FTX58eWytx1SVRXimjHWrFvyOMHI+nXi7A9xC0zy5JNxExOI3mz3ZR+o/56/NmA670ep/YzZfar69Puluvmyr7qlIimUqFVY4KWU1uZNgyyvstJNo/M+nP6FuuHS60JaM4lmNcW5oqibIddiWyCLKwlEW22D8vdq522KlVgS5lEzPZJSj/LJlJ0jn0U2x3wmGIV6ZYlUT32+/addeqM15MnnvHUk24z0r3HO2W6VVca/OjzZbtl9syQUl7kmC/bRsqdPdpmrzsT1Qx1xucaEtrS5+ZbVs5L6qC7XDtETGiXClpXRM8R1W6fQiwRxZY418OTCmjFoN8EJYVdiWxDaLCju90Xva4lsA2STSQ3ii2l7XMnpbG3+8pOFpCYLzvm0Xap7M+278++MZT2Pa05faY0XreEtOFgNZgUyW4oGs2e9N/KNtKtj+u6GUeGOuPzkYR2LPuICuw0zimkas2SGN13ocGFuX2oLbBTo9jnsoooiqLMZV8im6bR6VRxLWYPyRTYp27YAx+dlH6uTSTr9IQotjm2EcB0aOQJaHx+7JGonorvoFirKKob57mfAnEAcar1UwTbEdhCKj/f8jXnxmsL7lhEO2QbsYW2XRfIE9puZNEX1Q5ZgS6ZpYRTSrtzjp0jKoE0sT4nqj2H1OPWsnicExXmSi76jVFi7Etk96Sk8TOMrAZC9No3yFES2L6Bjt022SZSEsXu9pOj29Kym7pvIsIkC4lv2nVHWE8GQiYI79x7f8wmEotcpfiw7eWQoPZFs11s24h9HmIu7IDQNnm0c6La3fJlRbPdB6BSzimUxIfBSsdPbeecYjv1OEHLywJR7KUfkhRFUUrZlcgmxMW1L3odsoeYyLOURUQS2O5ARyOwT+uCTSR6blYUezoA8nASWI09EY0wKY0brfblXx7V7U7KOmDdr4V7f7Pvk/amcY7sqcAebCL9utXNFMuIG82WItkptpHJQEfLny0NhOzOWRba3ev4nG2hHYpqK2WsIcpyo9nA+G9YtP2FxLZp99wCew61Pl8V74qizGV3d2t3sGNXliauU+wh4/WwwHZ92CGbSE4U29S3BzyaMnHZtYr48OTLjlJR1JX+1NxYIhaY+rKBuGXErpcz4FHqi7GNGEIDIecIbXvZjWqr2F5fUOVEs0tFZpbXO1MU12oj9kBQI9NKaRRbUZZEv4FKiF3dpcdRT7+4BqYeasBvD+nWywW2NOmMzyYinpcTxXazhUgzQLrnObZ/BHzZvjpwrCGBaLaYS9uDNG36sG1YDk0w1DivPl+2vU1ajgnu1Gi2IebPriG0fVHtPXpec1lbQM05fu7nU1Non9q0xHLOv1xifQudW+0otsTaUetaVihFUfbHrkQ2MPVjS+I6Fr0uFdjDMcZiepJlRMg0YvcvFsXujj2OYnfnGrGKIODHljKOOPv0K+Jyckq/AKNsIrbAtj8/QThLDIJ72oZrGXFvjiadX+5N05dtxPVn1xLaoai2va+ST6lgSo1m+5gjOLf2cJXSn5LznRPFXvvBTLma6LdO8TF3WvXVmEwKIkSuAUeUCBPM5AhsaaCjfUw3Wp0y2FGKYrtWkGl0W07r5/Nju7gDJLdC0wDHo1vWTa9uZn4006qP6tAwxToQn+FxNKV66KbcT61uplu3Z9Gjhk5Trpvypun6yO3QLzO7o9n/NLMjEdA4Zae+cF9fbsNevmqkzNBYOhNkjRkkbXyzOFIjz/oY22a3CyBphsmlSMqAUklg12bJqLWKfEVRbHYVySZKj1wD8ej1Kers5MHOEdiSDzs2dXr0PBszGNPNYz0W26NId8AaEkz5drK82LaRZb8WdutSEHCwiYyj2j5f9mR5YhMZn48ZAJk9EY1lG5ls8/iz3dR+9nmYiLZpNzWq7WYgUeJUjVxnRLNLJmNJ/VzXiGynHrOmRWROFFtFr3Iu9JumSOxKZBuMaA6Ja8l7HbKHuBPNuPuGBPbpuJ5sIqVR7G7fvl4zjW4P26XMIR5fduPYR0YHi5Qlpe+zrR92eXi/fJvIVMS6lpHU1H1eX3YzeLNHfRBsI64/25dxRBLaYvmonfF7ZG9XthN1zLGNAPWE6NJi27SfnOmk8LzWssJs5fujKMrlsTORPfY/x8R1rj1ELHcE9tCOMwjS8WG7NpEcTBTblzt7OF/BKoKAH3t6oPHr6GCRPtfwaAee/Ycc2f26UHUQ3JZI94hrGzudX+xGKQ2CHJ1DI/uzu23zhXaqV3vLpEYYaw4QWzxynSmCfcQEaYnYriFWS9qK9bdEYNeOYqugVpZEvyWKyy492W6WDsl37dZzByvadXMEtm+g43hdiGYnRrElYW0PeDyVSVYRIOzHTkn1F4tmz6Qh4OhYSc07ZXzXJ49170cO+bLd5SPGHuzBk20c1Jj4bkM3ULfuSQgDaFuA2fZj955pIjQNep91d4bcdufVNoOv2vVoM4/LAZy82nxqa/BqXwVq+qRre67FY/TfXRefPxuI+7BTfNrS8c5J7GGglsA+ByqoFUWpxb4i2YSkyDXgj17XEtg+H/aou45NJAU7ii1aR5xoeTB1H6Z+bN+skDlp+SZERLjUcunhXF+2u5wTyQ55s3NtI6d1+4GvGX9XTV9Pvv9ARDslqn1VqSmCloiK5vqzgTSRusVfLlL6VVNg1/68lv4uafq+q4d+4orNrNs1Ef0QEd1HRB8loh/uy55ARHcT0f396+M9+76EiD5ORJ8gotdnHdcVMx4LSWMLZcF/XUNguz7skE0kN4oN4BTFnghuxyoiz+hYOPlMr+JE4b3QbJAnj7VJyUdme28DEbzeYzHt92ebdSmd37RO+pTrBl/+7O58xqn97HOyxbb5ad7OVewKbbvM9mrnsNY1uzRrRR9L0kD6SBHRWxHbqf2o6cHeUoT5XH251OtVUa4KxYqJiJ4D4PsBvADAtwD4TiK6GcDrAdzDzDcDuKdfd/c9APgZAH8DwDcBeBURfVPScZ3ItW9gY2r02ohhcWr1RIF96luiTcSHG8WWhHWKVQTA4MceH2Bcz80sUtUWMr0JNRhHbFORfNn2FOuhLCOS79qNUl9rAgMfPcLbFsd2mTsQEogL7VG5ENU25VJUO4e1rtm1WDPqGbI61JgZcS2xnXPcUoGdYxOZI3a3nqHkql2vl8R2HgeVtZmjqp4N4NeZ+QvM/CiA9wF4BYCXAbirr3MXgJcL+74AwCeY+ZPM/BcA3tbvF++wYAtJEdcp9hDTRldPFtj2cYc+keOZDttEUqPYXVuhrCNC1Nrqe1c+FtTFLOBRMPcuc0/1peyzOXhsIiHLiF3mpvNLxWcbcdP6LSW0fWI7k1Wu2Rykn9e3FMGUyLWNAHGhnSu2lxTcuceI1S0R2FkPODv8DnnY/PWqKEqYOcrpPgAvIqInEtF1AF4K4CYAT2bmhwCgf71B2PfrAPyRtf5AXxbE/vvrZhaRBjZ25YO4riGw7YGOdj5se1uOTcTupxvFbiT7iCvILatIX2E4boqFpBlHsXlQgqf25zB37JIkuO3lmGUkNWVfLJrt9knyX4/SF9pCfKbQdqPabvsZnP2aDbFWFHIRH3ZloQ3kP0TZYniu6C5tJ1a/psBeS0yfMVvOpq5XJY9dPtYp1SnOLsLMHyOiNwK4G8DnAXwIwKOJu0vfP3H4PBHdDuD2fvWLL/nEB+7L7evGuB7AI2t3YiaXcA7AZZzHs1IrnuOada/Xn/n3btn79QpcxvdEz2EbbOp6BabX7GOvu27v1+wlfE/0HLZD8jUrMSuFHzP/HICfAwAi+q/RPS1/iohuZOaHiOhGAA8Luz6A7onc8FQAD3qOcQeAO/pj3MvMt87p89roOWyHSzgPIro3p/7S1+ylXa/AZZyHnsM22Nr12h/joq5ZPYdtcAnnAORfsy5zs4vc0L8+DcB3AXgrgHcBeHVf5dUA3ins+psAbiaiZxDRlwN4Zb+foigLotesouwHvV4VZd/MnYzm7UT0RABfAvBaZv4cEb0BwC8R0WsA/CGA7wEAInoKgDcz80uZ+VEieh2AXwZwAPAWZv7ozL4oihJHr1lF2Q96vSrKjplrF3mhUPYZAC8Wyh9EN3DDrL8HwHsyD3lHbh83iJ7DdriE88g6hzNfs5fw/gKXcR56Dttgy9drdv82ip7DNriEcwBmngexMAWwoiiKoiiKoijlXPEJmhVFURRFURSlPpsV2XOmk90KnnP4cSL6YyL6YP/vpZFmzg4RvYWIHiai+6wy73tPRD/ST937cSL6jnV6PSbnHIjo6UT059Zn8k/X6/mA5xy+p/8+tUR0q1N/1c9Br9l1uITrFdBr9tyfhV6v63EJ16xer4mfAzNv7h+A56BLxH8dOt/4/wbgZgA/CeD1fZ3XA3jj2n0tOIcfB/AP1u5fpO8vAvA8APdZZeJ7j27K3g8BeAyAZwD4PQCHnZ3D0+16W/nnOYdno8vb+S8A3GqVr/o56DW7ue/Jrq7XgvPQa3ZeP/V63d73ZFfXrF6vaZ/DViPZc6aT3Qq+c9g8zPx+AJ91in3v/csAvI2Zv8jMvw/gE+im9F2VzHPYJNI5MPPHmPnjQvW1Pwe9ZlfiEq5XQK9ZnPez0Ot1RS7hmtXrNe1z2KrInjOd7FbwnQMAvI6IPtz/VLHpn+MsfO/9nqbvDX1/nkFEHyCi9xHRZET/Dlj7c9BrdltcwvUK6DW7FHq9bo9LuGb1enXYpMhm5o8BMNPJvhd508lugsA5/CyAZwK4BcBDAH5qpS7WInn63g3zEICnMfO3AvhPAfwiEX3Nyn3KZdXPQa/Z3XAJ1yug1+ws9HrdFZdwzV7Z63WTIhvoppNl5ucx84vQhfPvRz+dLACQfzrZzSCdAzN/ipmPzNwCeBM28LNPIr73Pnn63g0gnkP/889n+uXfQue1+sbVelnG6p+DXrOb4hKuV0Cv2cXQ63VzXMI1q9erw2ZFNpVPJ7sZpHMwX8CeV6D7yWsP+N77dwF4JRE9hoiegW7gyW+s0L8UxHMgoicR0aFf/np05/DJVXpYzuqfg16zm+ISrldAr9nF0Ot1c1zCNavXq0vpqMyl/wH4PwH8NrqfgF7clz0RwD3onrjvAfCEtftZcA4/D+AjAD7cf2g3rt1Pod9vRffzzpfQPb29JvTeA/hRdE+mHwfwN9buf+45APhuAB/tP6f/G8DfXLv/gXN4Rb/8RQCfAvDLW/kc9Jrd1PdkV9dr7nnoNbvYd12v1/W+J7u6ZvV6TfscdMZHRVEURVEURanMZu0iiqIoiqIoirJXVGQriqIoiqIoSmVUZCuKoiiKoihKZVRkK4qiKIqiKEplVGQriqIoiqIoSmVUZCuKoiiKoihKZVRkK4qiKIqiKEplVGQriqIoiqIoSmX+f1xID9xUE/4kAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_n(n, w = 0)\n",
    "plot_n(n, w = 1)\n",
    "\n",
    "import scipy.io\n",
    "a = np.arange(20)\n",
    "mdic = {\"X\": n[0, :, :, :], \"Y\": n[1, :, :, :], \"Z\": n[2, :, :, :]}\n",
    "scipy.io.savemat('texture.mat', mdic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nm = np.mean(n, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x129ac6ed0>"
      ]
     },
     "execution_count": 317,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fsv1l5xh2bHld3CrcgjVmGWJmV5MZT3HeW6PtJ4CfGHLsO4F3NlKRgI9AWVG6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\njuM4gIuh4zgO4GLoOI4DwP8HAlxi7YftdV8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x127e33c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imshow(Nm[2].T, origin = 'lower', vmin = -1, vmax = 1., cmap = cm.RdBu)\n",
    "title('Z')\n",
    "colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x12b928590>"
      ]
     },
     "execution_count": 318,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OTFIT1s3LjsROLY/VNkW7DgBA54oew/ygIbu5wvxYmV9godo6U5MjYXI8acns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\nP+y46BIsKQ58AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12a3a9dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imshow(colorize(Nm[0] + 1j*Nm[1]), origin = 'lower', interpolation = 'bicubic')\n",
    "colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x12ad90790>"
      ]
     },
     "execution_count": 320,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jXEga85+TBJoNLP/cSIL1l7BYHDOC4LVSyDKUZtCK4pfXS0HxMQa9CSQsFkm3HtcPA3Nv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\nHcdxSnBxdBzHKeH/A0jtQCkATo10AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1258c9490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e, f = F(n, Vqr)\n",
    "imshow(e.T-(uxy))\n",
    "colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
